Does snow have special meaning in this novel?

Now Ellen liked to read Sir Walter Scott and Dickens and Hans Andersen to the children before sending them upstairs, and one chilly March evening she read "The Snow Queen." Listening to it, it came to Joel that he had a lot in common with Little Kay, whose outlook was twisted when a splinter from the Sprite's evil mirror infected his eye, changing his heart into a lump of bitter ice: suppose, he thought, hearing Ellen's gentle voice and watching the fifirelight warm his cousins' faces, suppose, like Little Kay, he also were spirited offff to the Snow Queen's frozen palace? What living soul would then brave robber barons for his rescue? And there was no one, really no one.