Elizabeth Lowry has a great essay in the TLS (yes, it's online, too) on Angela Carter's Fairy Tales (a collection which is possibly only being released in the UK?).
It includes this perceptive discussion of The Snow Queen, which is my absolute favorite Hans Christian Andersen story of all time (from it I've borrowed the title & rough plot of the sequel to the novel I've just finished):
Unlike the narrators in Carter's collection, Andersen, as A. S. Byatt put it in a Keatsian phrase, has 'designs on the reader'. Take 'The Snow Queen', his passionate and tormented fable about an imprisoned self, written in 1845. Andersen's tale is built out of the emblems - ice, mirrors, the purity of snow - common to a group of stories about Snow White, but it refashions them into a terrifying vision that is unique. Kay and Gerda are childhood companions, until a splinter from a magical distorting mirror enters Kay's eye and his heart. He puts away his childish games and begins to spend all his time with a magnifying glass, admiring the perfect geometry of snowflakes, and doing mental arithmetic and fractions. One day he is claimed by the Snow Queen, a dazzlingly 'lovely and intelligent' woman made of ice, who keeps him as a willing prisoner in her cold palace beside a frozen lake, called 'The Mirror of Reason', that is shattered into pieces like a giant jigsaw puzzle. After many misadventures Gerda at last manages to find Kay, but he remains indifferent to her distress, absorbed as he is in solving the puzzle of the lake. It is only when Gerda begins to cry, and her hot tears melt the ice in Kay's heart, that he recognizes her, and in turn sheds tears that wash the splinter of glass out of his eye. At that moment the pieces of the shattered lake reconfigure themselves to spell 'Eternity'. In the space of a few paragraphs Andersen brings Kay and Gerda seamlessly home, where everything looks as it used to and they take their old childhood seats, although they themselves have become a man and woman. Gerda and Kay have triumphed over the mystery of time by preserving their innocence in adulthood.
This most unnerving story has all the stock elements of the traditional fairy tale: the fraught journey that is growing up, the opposition between purity and corruption, the stress on the importance of loyalty to those we love; but it is also, surely, about the seductive lure of the life of the intellect, the – to the creative artist – most tantalizing promise of aesthetic perfection and total freedom from distracting human ties. The Snow Queen, shimmering, flawless and aloof, is as desirable as she is dangerous, and one feels Andersen’s own attraction to her even as he pushes home the story’s expected moral. Far from recycling the fairy-tale conventions that lay to hand, Andersen has remixed their colours and given them a new and ambivalent intensity.
(I have always taken the story to be a fable of female masochism, though; Gerda following Kay despite his coldness and cruelty.)