There's not a specific elevation; it all depends on many factors such as weather and snowfall. Typically, if its mild mulies and elk will remain at higher elevations until snowfall drives them down.
One of the problems you have is that the big, older bucks will go nocturnal. They been there before and the increased activity will effect them. Once elk hunters start, it will only get worse.
Not sure what part of wyoming, But if it is the far west, Elk will be above timber line till the snow pushes them out. The smart big bucks will probably be timbered up from sheep and bow hunters.
The one where all the animals are. I wouldnt look for a specific elevation, because the deer will be at different elevations in different areas... I can't speak concerning the elk.