I've had experience with horses on trails in a few places I've lived.
- The horse owners think they ALWAYS have the right of way, going so far to yell at you if you don't slow to a crawl to not "spook" their horses. That's the most benign part.
- Horses crap all over trails, and unlike dog owners, horse owners never stop to pick it up. Horse dung is big and disgusting.
-Horse riders always go very slow, like a walking pace. They aren't galloping through the trails actually training their animals for a race, they are out for a joy ride just to show off how rich they are.
-Horse people are generally uncomfortable to be around. Talking to them, you get a sense that there is something off about them. Maybe if I'd had more than a short conversation with these people, I could put my finger on exactly what it is, but I've never had, you want to extricate yourself when you feel there is something off.
-The worst part is the crap
So in summary, I don't think horses should be allowed on any trails, save in the remotest, least used areas.