It's about a girl with no name. Her mother hadn't wanted another daughter, so she had refused to name her. She lives in a land that had been cursed with bad snow storms for as long as anyone can remember.
One day she is lucky enough to meet a magic reindeer who's legends say that anyone who is able to catch it can make a wish for anything in the world. She wishes for a name, which isn't revealed until the very end. When she's 16 (if I remember correctly) she is taken away by a great isbjorn (polar bear) to a palace made of ice where she must live for a year and a day. As she lives there, she learns more about the mystery of the palace and the isbjorn, but sadly her curiosity is costing her loving servants their lives.
If I say much more, I'll give away the whole book, which would spoil the ending, making this stunning story less stunning. It has a great, romantic, creative, beautiful happy ending, but not in a stupid way.
This book is based on the fairy tale "East of the Sun, West of the Moon", which, if you read it will spoil the whole entire story.