I've seen mountain goats of cliff faces where I wouldn't go unless I was roped up, and I've seen them in the bottom of valleys drinking water from the river, and even licking salt off highways.
When I shot my goat, the season opened in early September but I didn't start hunting them until mid November when they had their long and thick winter hair. The mountain that I shot my goat on was at lease a 45 degree slope with scattered vertical cliffs that I had to detour around. The day that I got him it was -5* F and knee deep snow where I started up. Previous scouting on that mountain with no snow and decent temperatures, I could hike to the top in about an hour. The day I shot him it took me 3 hours to get to the top.
In the few years after I shot my goat, 3 of my friends drew permits in that unit and they all shot their goats in the bottom of the valley, about an half hours walk from the road.
Before my Mon passed, she wanted to do one last trip to the top of Mt Evans, west of Denver. There is a paved road to within a couple hundred yards of the 14,265' summit. On the drive up we saw goats on 60-80 degree cliffs, and goats on the less than 20 deg grass slopes above timberline.