So Elsa leaves the castle ON FOOT, unwittingly starting a permanent winter. She leaves an easy-to-follow path of snow and ice. Minutes later, Anna pursues her, on a HORSE. Anna should have caught up to her rather quickly. But that would not serve the rest of the script.

Disney spent years coming up with a good story and script that would create a successful film. (The story development is an interesting read.) The film's success far exceeded their expectations. There is a LOT of humor that would appeal to adults, some of it at the expense of Disney's animated classics. I highly recommend it.