RE: Alaska Dall Sheep
I agree with the other posts. I went in August of 02 (seems like I started around the 10-14 or so) and we were in a fair amount of snow (and freezing rain and freezing rain and other fun stuff). I went up in the Brooks though, and I suppose the weather would normally be a bit worse up there.
Have a great time! It's an outstanding hunting experience. Oh, and start jogging or using a nordic track!
Edit - just wanted to add that we even got hung up for an extra day flying from Fairbanks to our base camp. Some other hunters we talked to in Fairbanks were held up for a lot more than one day.