When I think high country, I think above the timberline. Usually not a lot of water there and lots of rocky slopes, very similiar to sheep areas. My experience is that the deer like to stay just above the tree line, especially near green areas. Green means water and some brouse. The trees also give them an escape area for more cover. During the summer, the higher up they go means cooler temps and fewer insects to bother them. Look in shady draws during the heat of the day. If you can do some scouting, do it with your spotting scope, look for well used game trails and available water and green areas on the rocky slopes. Above all be patient. Unless you can see a buck bedded down or feeding, he will probably see you before you can see him!
My favorite areas to hunt these critters is above the timberline. I have a couple of areas in California's High Sierras that I have killed some real nice bucks above the trees. Look at my albums for a few. Most were shot above 9,000'.