I have always cleaned my wool only when I get blood on it. Other than that I let it dry and hang outside then brush off mud/dirt. Wool has a natural ability to shed odor from what I've read.
When it does NEED cleaning, I wash it in cold water, usually in the tub with a non scented non UV soap. Rinse well, and hang or lay flat to dry. Keep it away from heat, period. It will take a day or so to dry, and when you get the chance, stretch it every which way as it is drying by hand. If it is freezing out, I lay it to dry in my basement away from all cooking and day to day odors. When dry it goes in my cedar lined hunting closet. As long as you use the wind, you'll be fine hunting. Keep clean and as scent free as possible, but dont freak out. I shot a seven point one year from a tree stand. The wind was good, but as I was sitting before the deer came through I smelled crap. I stepped in a pile left by a dog on the way in in the dark. I was horrified, but about ten minutes after realizing this, a gorgeous seven point came right down my shooting lane never smelling a thing till I snuck an arrow in him.
I have never dry cleaned anything, even when the tags require it.