I had the tag last year. Fun hunt. We saw different bucks daily. Yes, the weather will play a factor and some snow would be great, but too much snow and you'll be limited on available roads. Last year we got about 14" of snow on the evening of the second to last day of the hunt. I met 3 tag holders on the last day of the hunt who hadn't filled their tags yet and were limited to the roads in the bottom of the canyons. That would make for a tough hunt. You want to get high and spend most of the day glassing the canyons.
Probably the last 5 days, if that's all you've got and hope the weather cooperates. Hopefully you can get over there on the weekends also. I spent 11 days in there on 3 trips and wish I could have spent more time.