I've had a problem with the wind in the past, but found something that works for me.
I've tried a knit hat, but not warm enough. Finally I had to get out my really, really warm (ugly) hat. When I lived in Alaska, a friend of mine used to make hats out of fox fur. She gave me the pattern and I made a "test hat" with pendelton wool, polar fleece and I think thinsulate (it's been a long time). I tied up the ear flaps, but pulled it down low and it was amazingly warm. So I'm sure a store bought bomber hat would work fine. We had wind chills of -35 this Saturday when I was in and it was no problem. My tub has a northwest exposure, with my house about 10' east of the tub. So my tub is totally exposed.
Also the water was 104 degrees. When I came in my face was red, but not cold.
It felt good.