What does Disney's movie "Frozen" have in common with Hans Christian Andersen's book, "The Snow Queen"?

Disney attributes its movie “Frozen” to being inspired by the Hans Christian Andersen story. But I see little in common.

Actually, C.S. Lewis’ “The Lion, Witch, and the Wardrobe” are far more similar to The Snow Queen.

To say the Disney movie was inspired by the Hans Christian Andersen tale is like saying The Wizard of Oz inspired The Lion, Witch and Wardrobe because they both have a lion and a witch.

The stories have almost nothing in common.