Like others have said, it's a tradeoff between good weather but short hair on an early hunt and possibly bad weather and long hair on a late hunt. When you're talking only 9-10" horns, the long hair is a big part of the trophy.
I got snowed out on my first goat hunt and ate the tag.
My second goat hunt was closer to home and I was able to go there throughtout the season. Early in the season I scouted but left my tag at home so I wouldn't be temped to shoot one with short hair.
When I finally shot my billy it was November 14th and it was -15* F and there was over 2' of snow on the ground. It took me over 3 hours to climb up to him where it only took one hour earlier in the season. But he had his full winter coat.