Horse riders should be accorded right of way over any mechanized means of transport, in the same way that sailboats have right of way over powerboats.
A sailboat is a mechanical device, a horse merely a collection of flight reflexes waiting to be triggered.
I rode in the mountains of Colorado, when I was at prep school in the Carbondale area. Give me a good mule any day. They are much more sure footed, far less likely to panic and kill themselves and their rider at the same time, etc.
There is the problem of horse exhaust, which all other trail users find vastly more objectionable than any motor exhaust.
Having said that, I have little sympathy for any hiker too dumb to keep its feet out of the horse exhaust piles on the trail.
A little courtesy wouldn’t kill any of the trail users.