I do wear a thin hat under the helmet almost every day in the Fall/Winter. I find that a hat absorves enough of the rain that I don’t need a helmet cover and soaks up sweat nicely as well. I’ve had my current hat for some years, I don’t even quite remember where I bought it or what brand it is.
It’s functional with a bit lighter fabric on the sides of my head, presumably for breathability. It does cover my ears, though I have to tug on it occasionally to make sure that it stays put. It’s not particularly warm or wind-proof, though gets the job done.
I thought I could use a step up from that in warmness and opted for the Craft Winter Hat. When the hat arrived in the mail, I was surprised that it was not as substantial or fleecy as I had expected given the name. The section that would cover the forehead is a different fabric which makes a lot of sense to me given that that is exactly where the most wind and rain is likely to “arrive”.
However, the forehead section was a bit loose in this L sizing. When I tucked the hat under my helmet and road around the block, this looseness was immediately palatable in some wind sneaking in under the bottom edge. The earflaps were also creeping upwards because the edge on the neck comes down to low, so with my head leaning back as I’m looking up, that edge pushes up.
I’m not sure whether these are issues that would be different in a size down, but I’m returning the hat for now, perhaps another item that’s better bought in person rather than on-line.