The Snow Queen/YMMV


 * Alternate Character Interpretation: The Snow Queen's reason for abducting Kai is never explicitly stated. While she probably just did so there'd be a plot, it's not uncommon for dramatized productions to make her a lonely Anti Villain who wanted Kai for a son.
 * I remember seeing an animated version once where the Snow Queen herself was under a curse, and captured Kai because she needed his help to solve the puzzle in order to break the curse.
 * Some versions have her a lonely villian who wants someone to rule with her.
 * This troper has seen a live action version where the Snow Queen actually kidnapped him because she knew about the mirror, and wanted to remove the shards -- it's so long ago that she can't remember if it was ever explained why she didn't just let him go after she was finished.
 * You may be thinking of Shelley Duvall's Faerie Tale Theatre which showed the Snow Queen to be protecting Kai and providing him with the opportunity to save himself. In that version, the troll's laboratory is on a raft floating around in outer space, and at the end the Snow Queen is shown to blow her wintry breath and send him sailing off far away.
 * At least one adaptation made the demon/Satan/troll/whatever that created the mirror doing so to show mankind how rotten it is, and had a My God What Have I Done moment when it broke. Of course, it almost certainly isn't what Hans Christian Andersen was going for.
 * Les Yay: Gerda and the Robber Girl; some translations even show the girl later doubting Kai is worth "going to the ends of the Earth for."
 * The Woobie: Gerda -- just look at what the girl goes through!
 * Iron Woobie: She takes it all in stride and wins in the end.