Father Frost (fairy tale)
It is Aarne-Thompson type 480, The Kind and the Unkind Girls. Others of this type include Shita-kiri Suzume, Diamonds and Toads, Mother Hulda, The Three Heads in the Well, The Three Little Men in the Wood, The Enchanted Wreath, The Old Witch, and The Two Caskets. Literary variants include The Three Fairies and Aurore and Aimée.
Once there was a woman had both a daughter of her own, whom she loved, and a step-daughter, whom she hated. One day, the woman ordered her husband to take her stepdaughter out into the winter fields and leave her there to die, and he obeys. Father Frost finds her there; she is polite and kind to him, so he gives her a chest full of beautiful things and fine garments. After a while, her stepmother sends her father to bring back the girl's body to be buried, which he also obeys. After a while, the family dog says that the girl is coming back, and that she is beautiful and happy.
When the stepmother sees what her stepdaughter has brought back, she orders her husband to take her own daughter out into the fields. Unlike before, this child is rude to Father Frost, and he freezes her to death. When her husband goes out to bring her back, the dog says that she will be buried. When the father brings back the body, the old woman weeps.