The Snow Maiden is a Russian fairy tale about a couple who wished for a child; one winter, they saw the other children making snowmen, and decided to make their own snow child. The snow child came to life in the form of a little girl. The snow maiden lived with the couple as their child, but was clearly supernatural-she grew quickly, was happiest in the cold, and avoided the fire. As spring came, she became sadder. The other children invited her to play in the forest, a game of jumping over a small fire. When it came the snow maiden's turn, she jumped, but evaporated into the air as she went over the fire and was never seen again.
The Snow Maiden list of tales on D. L. Ashliman's page has a couple other related tales from around the world; the plots are different (for example, most other versions seem to include a fatal romance), but they have something in common: tales involving supernatural winter females all seem to end very tragically.
The story of the same name ("Snegurochka," translated "The Snow Maiden") has been made into a play and an opera in Russia, but again the story is a bit different. The daughter of Spring and Frost wishes for human companionship, but is not capable of true love; once she does finally fall in love, her heart's warmth melts her and she dies. The story has been redone with a slightly happier ending, such as Ruth Sanderson who keeps the heroine alive, but as she learns to love she becomes a mortal human, so the ending is still bittersweet, as she will now have to die someday. These tales bear a resemblance to mermaid tales, in which romances are almost always doomed.
Illustrations by Ruth Sanderson
The Snow Maiden used to be commonly seen in Russia at Christmas in the form of ornaments and decorations; but when the celebration of Christmas was discouraged after the Russian Revolution (it was too bourgeois and religious), she was moved to New Year's, which was allowed in 1935. She has been associated with being the daughter of Ded Moroz, or Grandfather Frost, a Russian gift-giving version of Santa Claus who delivered presents on New Year's Eve.
Ukrainian Ded Moroz
Also, doesn't this Sanderson illustration for "Snow Princess" scream "Beauty and the Beast" to you?