I quite often wear a bandana, or as I have heard it called "do-rag" "drug helmet" or "babushka" !! It absorbs the sweat, keeps my helmet from moving around at all, and looks ok when I take the helmet off (but wet with sweat)

For the winter, I have a hood type deal that has a fleece neck attached. I LOVE that under my riding or biking helmet. If I get too warm, I can pull the hood down and just have the neck part.

Laura