In one story, she is the daughter of Spring and Frost, who yearns for the companionship of mortal humans. She grows to like a shepherd named Lel, but her heart is unable to know love. Her mother takes pity and gives her this ability, but as soon as she falls in love, her heart warms up and she melts.
another version as found on this site: http://www.geocities.com/Athens/Delphi/6422/tale.html
Snow Maiden
Once upon a time there was an old man and his wife.
They had everything they wanted,
A cow, a sheep, and a cat on the hearth,
but they didn't have any children.
Often they were sad and grieved.
One day during winter the white snow fell up to their knees.
The neighbor's children rushed out onto the street.
They slid on their sleds and threw snowballs,
and began to make a snowman.
Grandfather looked out of the window,
watched, and said to Grandmother:
"Well, wife, we sit here looking at the neighbor's children in our old age,"
"Let's you and I go out and build a snowman too."
And the old lady became merry as well.
"Well, let's go, Grandfather, onto the street."
"but why build a snowman, when I already have you?"
"Let's build a daughter, Snyegurochka!" (Snow Maiden)
No sooner said than done!
The old people went out into the garden and began to build a daughter.
They used two deep blue beads for eyes,
made two dimples in her cheeks,
and a piece of red ribbon for her mouth.
How good, their snow daughter, Snyegurochka.
Grandmother and grandfather looked and looked at her,
they loved her, and couldn't take their eyes off of her.
All of a sudden Snyegurochka's mouth began to smile,
her hair began to curl.
She began to move her arms and legs and then she walked through the garden and into the izba!(small wooden house)
Grandmother and grandfather couldn't believe their eyes,
they were so surprised they couldn't move!
"Grandfather!" cried Grandmother,
"Yes, it is, we have a living daughter, our dear little Snyegurochka!"
And into the izba they rushed, and what a joy it was!
Snyegurochka grew, not by the day, but by the hour.
And with each day, Snyegurochka grew more beautiful.
Grandmother and grandfather wouldn't let her out of their sight.
They doted on her.
Snyegurochka was as white as the snow,
her eyes were like deep blue beads,
her blond hair reached down to her waist.
But Snyegurochka didn't have any color in her cheeks or lips.
Still, she was so beautiful!
Spring came,
the leaves came out on the trees,
the bees flew about the fields,
the skylark sang.
All the boys were as happy as could be,
and the girls sang gay songs of spring.
But Snyegurochka grew sadder and sadder,
She looked out of the window and wept.
Then came bright summer,
the flowers blossomed in the gardens,
the grain ripened in the fields.
Snyegurochka grew more and more sad,
she avoided the sun,
she would stay in the cool shady places,
and best of all, she liked the rain.
Grandmother and Grandfather were very worried,
They kept asking her:
"Are you ill, little daughter?"
"I am fine, Grandmother." she would answer,
but she remained in her corner, feeling sad,
she wouldn't walk on the street.
One day her friends came,
they were going into the forest to gather berries,
raspberries, bilberries, and wild strawberries.
They came and called to Snyegurochka:
"Come with us, do come Snyegurochka!"
Reluctant Snyegurochka was to go into the forest,
reluctant Snyegurochka was to go into the sun,
but Grandmother and Grandfather insisted:
"Go, go, Snyegurochka,"
"go, go, little daughter,"
"you will have fun with your friends."
Snyegurochka took a little basket,
and went into the forest with her friends.
Her friends walked about the forest,
wove garlands of flowers, and sang songs.
But Snyegurochka found a cool stream and sat by it,
she sat looking at it, and dipped her fingers in it,
playing with the droplets.
Evening came.
The girls played even more merrily,
wearing their garlands,
they built a bonfire and began jumping over it.
Reluctant was Snyegurochka,
to play with them at this.
Her friends kept asking her to join them,
so she walked up to the fire.
She stood ther trembling,
her face as white as could be,
her hair fell loose about her.
"Jump, Jump, Snyegurochka!
Cried her friends.
Snyegurochka took a deep breath and jumped!
Over the fire was a hissing sound,
and Snyegurochka....
VANISHED!!
Rising from the fire was a wisp of steam.
It formed a cloud, and rose higher and higher,
into the sky.
Snyegurochka had melted.
