I'm late to the party. Pardon me for reviving the thread.
I hike AND I ride a horse. Random thoughts...
While hiking, I will nearly ALWAYS try and step aside and ACTIVELY NOTIFY bikes, hikers, horses - ahead or behind me that they are clear to pass me. That gives me a chance to be a bit of a "hiking ambassador". Even if they are a buttuski, they might just think "Hey that hiker was considerate". If they don't think that, no problem. At least I got out of the way and didn't get hurt. Getting hurt/killed or not ALWAYS trumps rules/laws/etiquette.
While mounted on horseback, I'm a much more dangerous weapon. As with carrying any weapon, I need to always have that in mind. If a biker runs into me and my horse, a nearly solid wall of nearly 1300 lbs, the biker will lose every time. The horse may startle a bit but she's a half ton of leather covered muscle. You can hit most trained horses pretty darn hard and unless it's in the eyes or the gonads, they are simply annoyed. But annoyed or panic'd, they will hurt anything that runs into them. If the horse then gets aggressive, as in a biker gets off his bike and appears threatening, the horse will "fight or flight". If they fight, the aggressor might very likely die. If they flight, the aggressor may be showered with horse hooves and loose rocks. Picture running face first into one of those mats they mount on the wall behind a basketball goal in the gymnasium.
While mounted on horseback, I will NOT direct my horse into an unsafe area. Most horses wouldn't go there anyway, no matter how hard you tried. My horse won't step into Jumping Cholla, cactus, holes in the ground etc. MANY MANY MANY horses sense wet ground as a bottomless hole. They think it's not just wet ground, it's a hole that will swallow them up.
IF you're passing me on a bicycle in either direction while I'm mounted, I may stick my size 11 boot with spur out in the path of your face. It will never be intentional. But I may do it because I'm losing balance, because my horse forces me in that direction etc.
I have served as paramedic to sanctioned mountain bike races many, many times. The rule there has always been (to the bike racers) "Even though you're in a race, you MUST yield to hikers and horses. If you don't, you're disqualified". I have seen bikers in the lead stop, get off their bikes and get out of the way of horses and mules. The equestrians didn't pick an ideal day for a horseback ride, but they are within their right to ride and the bikes are NOT within their right to disregard the trail rules just because they are in a race.
Bottom line for me, hiking or horseback, I'll try my darndest to yield to anyone. But I will NOT put myself in danger. And if I'm in danger, pedestrian or equestrian, and YOU are the threat/reason, YOU will lose. You may get seriously hurt, but you'll have a paramedic very close by..

We may also end up in court if you feel that my reaching out and pushing you out of my way and into a Yucca was some kind of criminal act. I'll take the risk. My horse won't care. She won't go to court. Likely the human vs horse encounter will be so overwhelming that court won't be needed. Only the coroner or ICU.
Sgt Lumpy - n0eq