I am not sure what you mean by "batting fleece" .... if it is regular fleece, like is used in clothing, then yes, you could use it. If it is a regular batting, no, I wouldn't use it and would look for something that would last and look better.
I like your idea to insert for Santa's beard and coat trim...
...........how about a fake fur or minkey?
Little girls and adults too would love the realistic feel of that ... far nicer than any fleece could ever give!