I used to use a merino wool neck gaiter as an open hat. That would keep my ears warm, and absorb sweat from my brow. The downside is that it was wonderful, and I'd use it every time I went out in the cold, so, eventually, I lost it in the snow on the way back from a hike to Annette Lake. Not long after that, I got a wool buff.

Yep, one of those. They make a wool one, the fabric is extremely light weight, but long, so there's a lot of room to get the right amount of insulation, but not too much.