In may be purely aesthetic, with no basis, but as a hiker I hate sharing a trail with cyclists. In a weird unsubstantiated way, I feel like horses are like other hikers. I've never had a horse like, gallop by me on a trial.
This is the number one reason why I hate sharing trails with cyclists. I've never seen a horse going over 6MPH, which is a light jogging speed, and they tend to go even slower downhill. Set a universal speed limit of 10mph on the trail at all times, which is a reasonable upper limit for horses and trail runners, and I don't think you'd see many cyclists.