Andrew Lang included it, as "The Story of King Frost", in The Yellow Fairy Book (1894).
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.
Father Frost finds her there, and because the girl is polite and kind to him, he gives her a chest full of beautiful jewels and fine garments.
Consumed by greed and envy, the woman orders her husband to take her own daughter to the same place, but when found by Father Frost the woman's daughter is rude and unkind to him, and he is inclined to punish rather than reward her.
The father finds her frozen to death at the foot of the tree and carries her body back to her grief-stricken mother.