We live at 6500 ft. elevation and regularly ride at 7500 ft, sometimes above. I don't know about horses coming from lower areas, but our horses that live here are just fine (and they were originally from lower areas). We never even think about the elevation being an issue. I don't know how long it takes to adjust though.
When I moved up here I never noticed a change in elevation affecting me at all, but I guess I was about 25 yrs. old at the time. The only thing I notice now is that if we travel to lower areas, the air seems really stuffy and stinky to me!
I guess that wasn't much help, lol!