My horse was born in mountains so no real problems.... but I would guess meeting mountian bikers and scary looking (to the hroses) hikers on the trail. And im guessing quads, and water could be a problem too.
Take a look at a NATRC competitive trail ride. They judge trail riders on both horsemanship and on the horse. I would think almost everything they judge on would be good information for people wanted to get into trail riding. In fact I used to tell folks that they should attend 2-3 NATRC rides just to learn how to take care of their horses on the trail. It's great experience.
Things that I make sure my horses know.
1.Stand while I mount. (No matter how hard it is for the person to mount. If I fall off and break an arm, sprain an ankle etc and I'm struggling to get aboard, I want that horse to stand still until I'm in the saddle)
2. Stop when I ask them to stop. Not 2-3 steps after I ask. I've seen too many horses get tangled in barb wire, step into a bog or go down in quicksand. If they had just stopped and stood still when the riders asked, most wouldn't have had a problem. The horse in this picture was the 5th horse to cross this steam. The first three had no problem, the 4th horses started to pump up the mud and liquidfy it. The 5th horse took one step and dropped his whole front end into quicksand. See the rider cleaning the mud out of his eys, nose and ears.
3. My horse all learn to hobble and tie to trees, highlines etc. If I want to get off and eat lunch, I often hobble my horses so they can graze while I'm off. When I camp, I highline or tie to the trailer. I don't want them beating up the side of my trailer because they are bored.
4. I teach all my horses pony. I don't want to have problems trying to lead a horse if I need to help somebody else. I don't want my horse freaking out, because he got a rope under his tail, because the horse I'm pnying is too close etc. My horses all know how to be the lead and how to be led. I frequently shoot deer and elk and have to ride a horse and lead a 2nd or 3rd horse to the kill site, load a dead animal on those horses and lead them back to camp or the truck.