I'm just wearing a hat / beanie
When I need real protection from the cold, I find that nothing beats a beanie or toque or knitted hat. I think the same design goes by all those names depending on where you live. Get a good one though, because the cheaper ones give very little real protection. Try a sporting goods store like REI since they usually have good choices. Also, check out the SBG beanie now for sale.

I've got one on order.
On hot sunny days in the summer I might wear a hat for sun protection. Bare-headed for the rest of the time, unless it drops way below freezing. Then, if I'm going to be outside for I while, I might wear a woollen hat. I just hate having my head covered. No hair and no hat feels great on a cold day !