The weather is a big deal. I've had temps near 75-80, and snow in the same week in the high country in September here in Washington. Single digit lows at night and t-shirt weather during the day. Changes quickly too. If you camp where hikers and horse people have camped, firewood can be sparse, if you are wanting to build a fire. Mice are always in camp, so get used to putting food away when you are not eating, and cleaning any dishes immediately after eating.
I'm assuming by high mountain, that you are talking about the September wilderness area hunts. If so, my best advice to you would be to get out there and scout the areas that you think you want to be hunting in as soon as the conditions (snow levels) allow. 7mag brings up some good points about conditions and camping, and remember that the more comfortable your camp, the more likely you are to stay and enjoy yourselves. In regards to areas to hunt, I suggest that you try to find an area that isn't as easily accessed by hikers. Use maps, google earth, etc. to try and find a ridge or area that doesn't have a trail running down it, and you'll be more likely to find the deer you're looking for. Good luck, post pics.
Definitely want to spend as much time as possible scouting before the season starts. This will get you familiar with which gear works and which doesn't. Also alpine BT's will be more Muley like then their valley brothers. This means glassing so be prepared for that.
And of course be advised that the bugs can be really, really bad!
You need to do a little research for the wilderness area you are planning to hunt as well. Rules can be different, or specific for different area's. For example, some places, you are not allowed to have a fire over 6000 ft, there are rules about how close to a body of water you can camp. Some trail heads have a pass required for parking, and some have a use fee for the area.