I have not read "The Snow Queen", but I have read "The Little Mermaid". There are major departures. (It's Disney, after all.) I consider "The Little Mermaid" to be the greatest movie ever made.

Watch "Saving Mr. Banks". Near the end of the film, Tom Hanks' Walt Disney character gives a beautiful explanation for why Disney told stories the way he did and why the better Disney movies continue to be told they way they do, even after his death.