I hunt the mountains, I live at 8500' and hunt from 5000 to 12,500. There are not many coyotes at the higher elevations. Like others have said, less food. But, I have killed about a dozen above treeline which around here is about 12,100'.
I personally believe that there are far more coyotes around hay fields and farm land, especially where there is livestock. Hay fields produce grains, grains produce rodents. Steep country is harder to hunt in that finding a place that you can see some terrain is harder, and your calls do not carry as far. It is a lower odds proposition, but it can produce if you put in a lot of time. Most people do not hunt difficult country, so the odds of finding a coyote that has never been hunted goes up.
Above treeline, I have coyotes cover vast distances and lots of elevation to get to me, they obviously have not played the game before. I do not hunt heavy timber often as the calls do not carry very far and therefore you are not covering as much ground, and if they are 300 yards and closing, you will not know it, until they are there. I always wonder if they were coming but I just could not see them. I try to hunt the really brushy areas late in the season when a few feet of snow takes away their cover.