I know to avoid cotton for cold weather biking. Fleece is often
mentioned as a good middle layer. But I've seen "fleece" that is 80%
cotton and 20% polyester. And I've seen "fleece" that is 100%
polyester.
I'm assuming that the 80% cotton isn't a good idea whether it says
"fleece" or not. I guess "fleece" just means "soft and mushy".