I can't see that covering your pile will hurt, but I don't think it will help compost the materials more efficiently. Might help keep it tidy.
I doubt it will have any insulating qualities in freezing weather. Do be advised that the thin black product found at garden stores deteriorates much faster when exposed to the elements, vs lying flat covered with mulch as it's designed for. I confess I'm having trouble saying anything positive about that particular product — not fond of the stuff.
