It depends on the area. My local trail system used to allow horses but they’ve been banned since 2012. I assume this was due to the higher mountain biking, hiking, and running traffic. A little farther away is Big South Fork, where many horse trails are open to mountain bikes and foot traffic. As far as I know there isn’t much conflict between these groups, but it’s a big park with plenty of room for everyone. To answer your question, you shouldn’t ride on trails that specify “horses only” or “hikers only”, but if you’re going to ride one of these types of trails, (which you shouldn’t) ride the hiking trail. The reason for this is that some horses spook easily. A spooked horse can be very dangerous to its rider and to you. Remember, we nail pieces of metal to their hooves, and they can kick really hard. A mountain bike moving fast can be scary to a horse and it could buck its rider, kick the mountain biker, kick anyone else in reach, fall on someone, etc. Somebody riding a nervous horse might ride a horse only trail because it’s safer for them, the horse, and everyone else, as there are supposed to be fewer unfamiliar trail users to scare the horse. Best to be polite to other trail users, and not ride trails you’re not supposed to. Be a good example for other mountain bikers, and don’t give a bad example to someone who might want to take away our trail access.