I have read that you get better results if you cover your compost pile with a scrap piece of carpet year round. In the Summer it keeps the pile from drying out and when it's rainy it keeps it from getting soggy.

You do want to cover it to keep the rain off. The pile should be plenty damp as it is. Letting it get rained on will keep it too wet and cold over the winter. You can keep working the same pile over the winter if you like, or start a new one.