Skadi is not one of the best known or most popular of the gods and goddesses of the North, but she does have her devoted followers, and I will show that her presence is still felt among Northern people and their descendents.  We do not have a lot of information on her, and she is something of an outsider, belonging to the Aesir only by adoption and by marriage.  What we do know of her suggests a strong goddess, but not really a cozy one.  In fact, she makes people feel uneasy.
     If you have ever been out alone, far from any dwelling, at night in the hills or mountains on a cold, crisp night when the moon is bright, and lays a bluish sheen over the snow, an uncanny feeling comes over you that you are in an alien world, one not native to the human animal, and potentially deadly to him.  Skadi embodies that sense of dangerous otherness that pervades the winter landscape, for she is a goddess of the mountains and forests of wolves and game animals, of hunting and archery.  She is traveler over treacherous snow and ice.
     Old Germanic literature has few descriptions of people, and even fewer of gods, so that our sense of Skadi's appearance is either visionary or UPG (unsubstantiated personal gnosis).  There seems a consensus that she is tall and slim.  There is nothing particularly wintery in these traits; in fact, short and thick is best for dealing with cold, so those details do not come from logical deduction.  That she has very white skin is a more easily explained detail.  Most too see her as having intensely blue eyes, though some see her as dark eyed.  My own sense of her which is very strong, but has no other particular authority, is of a tall, slim, strongly featured woman with very white skin, very deep, very bright, dark blue eyes, and heavy, wavy black hair.  Not all details of this picture agree with everyone else's, but a surprising number of other people have said that this is their picture of her as well.
      The primary story we have concerning Skadi is of her winning Njord as a husband.  My translation of the Prose Edda is still under copyright, so I will give H.A. Guerber's retelling from Myths of the Norsemen:
     Shortly after Idun's return from Thrym-heim, and Thiassi's death within the bounds of Asgard, the assembled gods were greatly surprised and dismayed to see Skadi, the gian't daughter, appear one day in their midst, to demand satisfaction for her father's death.  Although the daughter of an ugly old Hrim-thurs, Skadi, the goddess of winter, was very beautiful indeed, in her silvery armour, with her glittering spear, sharp-pointed arrows, short white hunting dress, white fur leggings, and broad snowshoes; and the gods could not but recognize the justice of her claim, wherefore they offered the usual fine atonement.
     Skadi, however, was so angry that she at first refused this compromise, and sternly demanded a life for a life, until Loki, wishing to appease her wrath, and thinking that if he could only make her cold lips relax in a smile the rest would ben easy, began to play all manner of pranks.  Fastening a goat to himself by an invisible cord, he went through a series of antics, which were reproduced by the goat; and the sight was so grotesque that all the gods fairly shouted with merriment, and even Skadi was forced to smile.
     Taking advantage of this softened mood, the gods pointed to the fimament where her father's eyes glowed like radiant stars in the northern hemisphere.  They told her they had placed them there to show him all honour, and finally added that she might select as husband any of the gods present at the assembly, provided she were content to judge of their attractions by their naked feet.
     Blindfolded, so that she could see only the feet of the gods standing in a circle around her, Skadi looked about her and her gaze fell upon a pair of beautifully formed feet.  She felt sure they must belong to Balder, the god of light, whose bright face had charmed her, and she designated their owner as her choice.
     When the bandage was removed, however, she discovered to he chagrin that she had chosen Niord, to whom her troth was plighted; but notwithstanding her disappointment, she spent a happy honeymoon in Asgard, where all seemed to delight in doing her honour.  After this, Niord took his bride home to Noatun, where the monotonous sound of the waves, the shrieking of the gulls, and the cries of the seals so dusturbed Skadi's slumbers that she finally declared it was quite impossible for her to remain there any longer, and she implored her husband to take her back to her native Thrym-heim.
     Niord, anxious to please his new wife, consented to take her to Thrym-
heim and to dwell thee with her nine nights out of every twelve, providing she would spend the remaining three with him at Noatun; but when he reached the mountain region, the soughing of the wind in the pines, the thunder of the avalanches, the cracking of the ice, the roar of the waterfalls, and the howling of the wolves appeared to him as unbearable as the sound of the sea had seemed to his wife, and he cound not but rejoice each time when his period of exile was ended, and he found himself again at Noatum.
     For some time Nirod and Skadi, who are the personifications of summer and winter, alternated thus, the wife spending the three short summer months by the sea, and he reluctantly remaining with her in in Thrym-heim during the nine long winter months.  But, concluding at last that their tastes would never agree, they decided to part for ever, and returned to their respective homes.
     This charming retelling agrees generally with Snorri's briefer version.  One difference is that Snorri makes being made to laugh a condition that she sets, rather than an initiative of Loki's.  Snorri also does not have Njord's extra-generous agreemt to divide the year nine months in one place, and three in the other, which I suspect is an addition of this particular author.  In Snorri, they are to alternate, nine nights at Skadi's home in the mountains, and nine nights at Njord's home by the shore.  The prank by which Loki makes Skadi laugh, by the way, is to tie a string from his own balls to a goats beard and bound about the room in tandem with the goat.
     There is some question about Skadi's marriages and sexual relations, which Snorri does not entirely help.  He tells us that Njord had two children after his marriage to Skadi, Frey and Freya.  One might suppose they were a product of the union, except that he only says that Njord has them afterwards, which would be odd if Skadi were the mother.  In other contexts Snorri claims that they come with Njord from Vanaheim, and are the children of Njord and his sister.  Also, they are always spoken of strictly as Vanes.  We hear from the Edda that the Aesir gave Frey Alfheim as a tooth-gift, but the Alfs seem generally associated with the Vanir to begin with.  It is widely thought that Skadi, though sometimes called the mother of Frey and Freya is, in modern English, their stepmother.  The terms mother and father are applied not only to step-parents, but to mothers and fathers-in-law in the Edda and the sagas more freely than we are used to.  In Heimskringla, Snorri tells us that after the separation from Njord, Skadi married Odin and had numerous children, from one of which descends the line of Hladir jarls.  There is also a popular tradition that she married Uller, another winter divinity with which she would have had much in common.  Finally, there is Loki's accusation in Lokasenna that she slept with him, the murderer of her father.  Those of Loki's charges that we can make a clear judgement on seem to be true, so perhaps it is the case here as well.
     The prose passage at the beginning of Lokasenna tells us that Njord was at Aegir's feast along with his wife, Skadi, though we get the impression from Snorri that it was not a long-lasting relationship.  Still, she is behaving as a mother when in Skirnismal she is the one who sends Skirnir to enquire about Frey's mental state.  Skadi enters the quarrel at Aegir's feast with a prophecy of Loki's ultimate fate, then Loki taunts her with the killing of her father.  She responds by saying that from her sanctuaries and fields baneful advice will always come to him.  This reference to sanctuaries and fields seems to imply cult activity devoted to Skadi, an indication that she is an important divinity.  Also, Skadi is an element in a number of Swedish place-names, further indication of her importance.  Loki ends the exchange by claiming she spoke much more pleasantly when she invited him to her bed.  When Loki was captured and tied to the rock, both Lokasenna and Snorri agree that it was Skadi who placed the poisonous snake above Loki so it would drip venom on his face.
     Someone--I forget who--just after the Viking age stated that Freya was the only divinity that still had a hold on the minds of the people.  Skadi, though, still appears to live in the unconscious mind, because her image in somewhat garbled form continues to appear.  One example is Hans Christian Andersen's Snow Queen from his famous story, The Snow Queen.  Here is one brief description:  "The fur cloak and cap were all of snow.  It was a lady, tall and slim, and glittering."  A little later is this mythic sounding passage:  "Then away they flew over forests and lakes, over sea and land.  Round them whistled the cold wind, the wolves howled, and the snow hissed; over them flew the black shrieking crows.  But high up the moon shone large and bright, and thus Kay passed the long winter night.  In the day he slept at the Snow-Queen's feet."
     This is clearly the picture of a winter goddess, and like so many picture Skadi, she is tall and slim.  The picture here is a negative one, and suffused with a Christian dualism, but I think we already have some of the same feeling of strangeness and danger about Skadi that Andersen gives the Snow-Queen.  Andersen, however, has several agendas, not all of them mythic--for one thing, he makes her a proponent of geometric and abstract form, which he sees as scientific and cold, as opposed to the organic warmth of imagination and emotion.  This is a standard opposition for the nineteenth century and its uneasiness about modern science.  We get much the same symbolism is Dickens' Hard Times.  Her determination with the little boy is that he not be able to spell out love, and thus get free.  But at the same time, she is a mythic being, for at one point she is to fly south to dust Etna and Vesuvius with snow for the benefit of the next grape and lemon harvest.
     C.S. Lewis is more fully mythic than Andersen; his White Witch is the great opponent to his Christ-figure lion.  This is, in fact, a rather grander role than the Teutonic people ever gave the winter goddess.  This relatively popular book, The Lion, the Witch, and the Wardrobe, and the later books of the series have become suddenly much talked about due to a Disney movie.  (If it does to its charcters what Disney movies usually do, I'm glad it's not my side that's being propagandized for.)  Like Andersen, though, he has the usual Christian dualism, and symbolizes it much the same way.  In Lewis' case, however, the coldness of the White Witch is spiritual rather than scientific and analytic.  Why the White Witch as the great enemy of Christendom?  Maybe it's just a touch of mysogynism.  Or, maybe he has heard of Robert Graves' White Goddess, and Graves' desire to replace Christianity with what he considers the older religion, though a cynical person might call it Gravesism or Gardenerism.  Lewis is, of course, idealogically prevented from calling her a goddess, though he probably otherwise would.  She, we are told, is, like Skadi, a daughter of giants (and of Jinn as well).  One of the features of Skadi that I have no explanation for is why she is continuously identified as a daughter.  Women are likely to be lovers, mothers, sisters, and grandmothers as well, and Skadi is clearly three of these, but she is regularly idendtified as a daughter.
     We have the daughter identification again in Robert E. Howard's "The Frost Giant's Daughter."  This is a memorable story in the Conan series, and inspired one of the most memorable, and most often reproduced of Frazetta's paintings:
     Robert E. Howard has moments as a very good writer, and in this fairly simple story he achieves an almost mystical sense of winter's alien and inhuman beauty.  The Frost Giant's daughter, like other accounts of the winter goddess is slim and very white skinned.  This particular version of the winter goddess has red-gold hair and blue-grey eyes.  Here is a brief exchange between Conan and the Frost Giant's daughter:  "Tell me, woman, have you seen the flash of mail out across the snow-plains, or seen armed men moving upon the ice?"  "I have seen the hoar-frost glittering in the sun," she answered.  "I have heard the wind whispering across the everlasting snows."
     Unlike Andersen and Lewis, Howard does not have an idealogical agenda, which makes his story refreshing, but he does have some pulp fiction imperitives--to make the woman sexy and nearly naked, and to give the hero an adventure story full of violence and danger.  Thus this winter queen does seem to have a mythic dimension, as in the testimony of another character later in the story:  "Myself when a boy I saw her, when I lay half-slain on the bloody field of Wolraven.  I saw her walk among the dead in the snows, her naked body gleaming like ivory and her golden hair unbearably bright in the moonlight."  Somehow we don't quite expect that of Skadi, nor do we tend to agree with the rest of the story.  It turns out that she lures men from the battlefield deep into the mountains where they are set upon and killed by her brothers, to supply the heart for her father to eat.  Conan kills the brothers, as she escapes his embrace only by the Giant's intervention.  Skadi clearly does not have brothers, or it would have been their responsibility to take up arms and demand satisfaction for the death of Thiassi, rather than hers.  That she does so, though not especially a warrior goddess, says something about her nature and character.
     The story of Skadi's marriage is one of the best known of all the stories of the gods, and it is odd that there is no Eddaic poem dealing with it, though there may have been at one time, since Snorri does give a couple of stanzas in which Skadi and Njord complain alternately about each other's environments.  Snorri, himself, surprisingly does not tell this story either in any unified way.  He gives parts of the story in two different places in the Prose Edda.  I have therefore written an Edda-style poem about it in Fornyrdislag meter.  The one untypical feature of the poem is the physical description of the goddess, which is my own UPG, though not radically different than many others.

What man so fearless    the fells to cross,
And boldly set foot    on Bifrost way?

No man so fearless,    a maiden instead
Has boldly set foot    on Bifrost way.

Your eyes grow weak    from watching long
Surely no maid    of Embla's line,
No Jotun or Vane    would venture thus
Boldly to fare    so far alone.
Maid in truth,    but tall of frame,
Lath-slender,    long of stride.
She comes apace    across the fields,
And neither looks    to left or right.

Like raven's wing    her wavy hair,
Skin as fair    as frost at dawn,
Eyes bold,    blue as sky,
As sheen that glows    in glacial ice.

Weapons she bears,    and bow of yew,
But hunting I doubt    has drawn her here.
Wergild, not game,    I'd guess she seeks.
Far she comes    some claim to press.

Some evil deed    has drawn her here,
A brother killed,    or cunning theft.
Wicked your ways,    your wiles well-known--
Loki should bear    the blame alone.

A lot you say,    but little know;
For Thiassi's bane,    that blaze you lit,
All the gods    some guilt must bear.
Loki of all    is least to blame.
My wiles I used    your wills to serve,
When wide I flew    in falcon cloak,
Freya's gift,    grudgingly given,
To steal Idun    from Stormhome back.

By cunning I found,    and carried her off;
Thiasse came after    in eagle form.
Hard the race    we ran that day;
Many the dangers    for the maid I bore.

Proudly you speak,    praise you demand,
Undoing the deeds    you did at first,
But wiles will not    unweave your fate;
This maid you bane    will be one day.
     The traveler approached and told them that she was Skadi, the daughter of Thaisse, and that she had come to Asgard to seek compensation for the death of her father.  Loki and Heimdal led her to where the gods were gathered.
Far have you come;    fair be your welcome;
You shall not go    ungifted hence.
Rings and red gold    gladly we'll pay;
All that you ask    the Aesir will give.

Rings I have,    gold-roofed my hall;
Other than these    you owe for the slain.
Little you guess    my greatest wish.
A different payment    promise me now.

Rashly offered,    after rued;
Tell me first    what fee you seek.
If it gladden not    the grey wolf's kin,
Maiden, I promise    what payment you will.
Little the wolf    by my wish will gain.
Grant me this--    a god as mate.

Wisely spoken;    a woman alone
A man should get    to gladden her hall.

A second gift    of the gods I ask.
I've sorrowed much,    a maiden alone;
No laughter or son    fills Stormhome now;
Before I leave,    a laugh I want.

A laugh you'll have,    but who do you want?
Which of the gods    shall go with you?
Baldr of gods    is best of all,
The shining god    who gladdens all things.

His beauty's fame    bourne on the wind
Through worlds nine    to the north was blown.
All that I've heard    my heart has won;
First among gods     is Frigga's son.

My son is yet    too young to wed;
full soon it is    to seek a wife.
The choice besides,    should be his own;
It is not yours,    Jotun maid.
You promise much,    perform far less;
Too few the oaths    Odin has kept.

Blame me not    before I speak;
I've not denied    aught due to you.
But I require    one rule alone--
Choose by feet,    the face concealed.

Skadi agreed;    the gods lined up,
Behind a hanging    hid themselves,
feet bare    beneath the hem,
While Skadi stood    and studied long.
Well-formed  she thought    the feet all were,
But stopped at last,    and laughed with joy.
Here, she said,    must stand my love.
Here stands Baldr,    best of gods.

These are finest,    most fittingly shaped,
Clean as bone,    bright as morn,
White as ermine's    coat on snow.
Surely no other     owns the like.
     Freya stepped forward and drew the hanging aside, and all saw that it was not Baldr who had been chosen, but Njord.  Skadi was not greatly pleased.
Skadi choosing.  Although Skadi might not be the cutest or most bouncy of the goddesses, I wish the artist had not made her quite so grim.  I would also expect her clothing to be more suited to traveling over rough country.  Skadi, pictures, though are not so easy to come by.
False my eyes,    foolish my words,
Boasting my prize    ere bow was strung.
Crooked my arrow,    aim amiss,
Reckless my choice,    most wretched of maids.

Maiden, be cheerful;    your choice was good;
Wrongly you scorn    the richest of gods.
Great his treasure,    giver of rings;
Bringer of peace    and prosperous lives.

In feature and form    flawless of line,
He rules the wind,    the waves make calm,
His blessing is sought    by sailors all.
Bountiful the field    his breath has touched.
Subtle the weave    our wyrd has wrought;
In sleep I did    not dream of this,
Nor waking think    a wife to find,
But welcome to you,    bold Jotun maid.

Hard is fate;    my heart was set,
And yet I find    no fault in you.

What is your will;    I wait your choice;
Have my hand,    or have it not.

I'll take your hand,    though heart still lags,
Still backward looks    on Baldr's form.
The Norns alone    know what will be,
What luck lies in    the lot I've cast.
But though I have    a husband now,
One promise owed    by Odin yet,
May prove for him    a harder task;
My mind is not    to mirth inclined.

Then Loki came,    leading a goat,
Into the crowd,    capering about,
One rope end tied    around the horns,
The other wrapped    around his balls.

Loki would give,    the goat would pull,
Then Loki turn    tables around,
Bleating and squealing,    bouncing about,
Till loud the hall    with laughter rang.
Then Loki with    a leap and cry,
In Skadi's lap    lit with a thump,
And she, surprised    at such an end,
Loudly laughed    at Laufey's son.

So Skadi wed,    and weeks flew past,
Gladly feasting,    gods among,
With mirth an mead,    and many games,
Of chance or skill    or subtle mind.

Loud rang the harp    in high-roofed hall,
Songs of laughter,    love and war,
Of Jotun schemes    to steal Od's bride,
Or bright Iduna,    Bragi's joy.
Of Freya's loves    and Loki's pranks,
Of mighty Thor,    the thurses' bane,
And Odin's wandering    worlds through.
But then at last    leave-taking came.

And Skadi, proud,    much praised her home
Among the steeps    and snowy crags.
Njord preferred    more pleasant scenes,
His shining hall,    the shore beside.
So each would stay  at either home
Nine nights.  Njord complained,
"Mountains I hate;    howling of wolves
Is harsh compared    to cries of swans."

Then Skadi cried,    "How can I sleep
Beside the shore;    the shriek of birds
Keeps me awake,"  and went, therefore,
Back to the fells,    her father's home.
     Thus Njord and Skadi parted, though on friendly terms, but ever after she was accepted among the Aesir.  It is said by some that after parting from Njord she wedded Ullr.
     Snorri speaks of Skadi as traveling on skis and hunting with a bow.  Elsewhere she is called "snowshoe-dis."  The meaning of her name is uncertain, though some have tried to link it with a word for shadow.  Whether the name Scandinavia comes from her name is debatable--sk words are very common in North Germanic languages.  There are some sites on the internet that give a great deal more about the goddess, but this is clearly a mix of guesswork based on deduction and UPG.  One should not feel compelled to accept any of it that is not backed on the reader's part by a strong sense of its rightness.  Even this, I realize, is a treacherous guide, but sometimes necessary in dealing with divinities about whom too little written lore survives.