I have hunted NW Wyoming in October several times.
What I found is occasional rain, occasional snow, cool to cold nights, but it was dry most of the time.
I would NOT spend a lot of money on rain gear. I'd spend it on wool pants and maybe a goretex outer jacket, but that's about it. If it gets sloppy wet, I'd be really surprised.
It is NOT wet compared to the NW (Oregon, WA). The days will still see 50 or 60 degrees and nights will put down some frost. If a front moves in, it may rain a bit and / or snow, but not for extended periods unless it is a fluke storm and it will melt within a day or two.
Bottom line is that even if the chance of rain is low, if it does rain and you are not prepared, you will be miserable. I would not recommend solid vinyl rainsuits that don't breath. You would be sweating profusely immediately when walking in the mountains. Some people get by with a cheap poncho, but I have invested in some breathable raingear. You can spend an arm and a leg, but I got Cabelas packable rain suede jacket and pants for around $150 total. They are nonisulated and are roomy enough that you can put them on over other clothes/jackets. I probably only use them 1 out of 3 trips to the mountains, but they are worth their weight in gold when I need them.
The other item that you need to know is that your boots are more important than your raingear. They should be broken in well and I usually take 2 pair, one insulated and 1 noninsulated. If I had to take only 1 pair, it would probably be the unisulated one and use a good liner and thick wool sock. They definately should be a breathable/waterproof. Cold/wet feet will also make you miserable.
Want a quick and inexpensive call for Moose? Take an empty 32 ounce coffee can, and make a small slit in the bottom, only about a quarter inch. Then, take one of those really big red rubber bands, the ones that go around big folders. Cut the rubber band to make one long piece.
Now, thread one end of the band and tie a knot on the outside of the can so it won't pull through. Cut the band off on the other side so it is even with the top of the can.
Now, wet your finger,...