My coat doesn't have a hood. It's a heavily insulated leather jacket. It zips to the chin and has a full-length placket blocking the zipper, but no hood. Generally I just wear a wool/acrylic hat, and if it gets really cold I have that neoprene facemask.
I use a mug and a brush, the key is to get the right amount of water. I've found that even just quickly running water over the brush gives you too much water with the soap I use. I generally fill the mug partway with hot water, dunk the brush, then pour out the water and shake the brush. If I'm doing more than a couple passes, I usually need to work up more lather as well. Cream would probably be easier, since you can get more going at a time, I'm limited by how much my brush will pick up on the tips of the bristles.
