The Snow Queen (2005)

Kai and Gerda are very dear friends who have been living together since young. However, one wintry day, the Snow Queen appears stirring up snow and wind, and a sliver of mirror gets lodged into Kai's heart. Kai drives Gerda away in tears and the Snow Queen takes Kai away to her realm. The adults try to dissuade Gerda from pursuing Kai, saying that he is already dead. But determined to find Kai, Gerda set off on her own journey which is filled with trials and tribulations. Description taken from AnimeNewsNetwork