snow queen

snow queen from Hans Christian Andersen's tale.
She also seems to be the origin or inspiration for white witch in the chronicles of Narnia
And before disney's frozen turned into what it is now, it was supposed to be the snow queen story.
made me thought it would have been interesting if Elsa was actually related to the snow queen in old tales or maybe she can be the descendant of Kai and Gerda.
and maybe there was a remaining curse from the snow queen on Kai which could have caused the mystery power that Elsa's born with?