There are three types of fairy-tale re-tellings (1) those that miss the mark by a wide margin (2) those that feel quiet alright by changing some elements and updating others and reminding us why we loved those stories in the first place and (3) the very few that improve upon the originals and replace them in your personal canon.
Actually, the original I remember isn’t the Hans Christian Anderson story, which I know I read as a kid, but whose memory who overtaken by the breathtakingly beautiful Russian animation from 1957, which for me was the most definitive version until now. Despite not having seen this for years, I remembered the tension between Gerda and the bandit daughter despite this being a kids movie. There was something there, if extremely subtle at that.
Vernon aka Kingfisher marvelously took those elements from the original tale, embellished them and spun them into a tale that is still recognizably the Snow Queen, but also something different. The rough story skeleton is the same, but some of beats are subtly and sometimes not so subtly altered to change it from the girl setting out to get the guy to the story of the girl who grew into her own, saved a guy (lets not pretend that Kay isn’t an ass in all of the versions) and got the girl.
At the end of the story I felt utterly like cheering and happy and nodding in agreement. This is how you do a re-telling.