I was moved by the story of the Snow Queen after reading it from a non illustrated Hans Andersen Tales collection. This inspired me to purchase my own illustrated version so that I can share the story with my children whose attention spans are short without pictures to break up the text.
As an earlier reviewer has already outlined the chapters of the story, I'll keep the plot brief. The story tells of a little girl's long journey to rescue her beloved friend from the palace of the Snow Queen and release him from the spell that has turned his heart into a lump of ice and alter his personality.
The high point of this particular version of the story is the stunning illustrations by Christian Birmingham. Of all the illustrations that I have seen of the Snow Queen herself, which tend to portray her as scary and evil, I think that he captures her extremely well, beautiful and haunting but not necessarily wicked. On the front cover of the hardback version, the jacket is covered in silvery snowflakes with a circle -representing the hot coin on the window, peering at the Snow Queen who is
"dressed in a gown of white gauze, which looked like millions of starry snow-flakes linked together. She was fair and beautiful, but made of ice--shining and glittering ice. Still she was alive and her eyes sparkled like bright stars, but there was neither peace nor rest in their glance."
You can see more of the illustrations if you google Christian Birmingham books illustrated.
Finally, this is not an abridged version like you would get with many children's books and as a result you will not be able to finish it in one sitting if reading to a small child. I would also like to mention that because it is translated by Naomi Lewis, you can rest assured that you are getting a faithful translation of the original story.