I probably have more tolerance for horses than most because I have always loved horses and because I grew up horsepacking. I really don't mind the poop (it dries up fast). I also recognize that horse trails came first and that a significant amount of trail maintenance, especially at a farther distance from trailheads, is done by the Backcountry Horsemen and other volunteer groups. A lot of hikers seem to forget that!

Like aimless, I do mind when horses are tethered overnight in what would otherwise be a good camp place. That's especially an issue on the west side of the Cascades where camp sites are limited because of the amount of underbrush. I also mind when general "LNT" rules aren't followed or when trash is left behind, regardless of the mode of transport.

Phat, the horse survived for millennia by running first and asking questions later. It's the nature of the beast! Even the most gentle horse will spook on occasion, just as the sweetest, most loveable dog will bite if sufficiently provoked. There's also the issue that a horse cannot be trained for trail work by leaving him at home--the only place to train a horse for trail work is out on the trail. It's normally the group leader who will be riding the green horse. It doesn't hurt to give them some extra room--for your safety as well as that of the horse and rider.
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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey