Here in California, a lot of trails have signs with a triangular diagram, showing that cyclists should yield to hikers, and both cyclists and hikers should yield to people on horses. I don't have a problem with yielding to horses, but what is the logic behind this? Not to startle the horse? Not to get your feet stepped on? In general, what is the polite way for hikers to behave toward people on horseback?
In the Grand Canyon, it's because it's easier for a human to get off the trail than it is for a mule. I suspect the same reasoning applies in most places.
Generally "X gives way to Y" rules can be found not just on trails but on open water (steam gives way to sail) and in rivers and channels, even on city sidewalks. They seem to be based on these (potentially contradictory) reasons:
- slower movers should allow faster movers to pass them and carry on away (after catching up from behind)
- more nimble entities should nip aside where there isn't room for both entities
- those that cannot move in certain directions (sideways is hard for horses; sailboats can't turn arbitrarily) should be allowed to keep on going while the other entity does the difficult/impossible move instead
- those that can't go in some areas of the pathway (on the soft ground, into the trees, up a fence, in the shallow water) can have the right of way and the other entity can go to the margin or something to enable passing (in either direction)
In the case of horses and people, I see every one of these rules supporting that the person should get out of the way. Sure, in "steam gives way to sail" some of these are contradicted, because the rules point in different directions and they have to be reconciled somehow. But I don't see any logical reason why a larger, faster entity that can't do some of the things people can should be yielding to the slower yet more nimble human, who can do things like climbing a wall or fence to get out of the way.
Now, all that said, if this list determined the rules cyclists would be between people and horses, so horses would have priority always, then bikes, then people, and people would be ducking off the trail or climbing a fence to let bikes go by. But that's not the rule on your signs, so it's possible my logic doesn't apply.
The safe and courteous way to handle an encounter with stock (horses, donkeys, etc.) is to step off the trail to the downhill side, and also to talk to the riders. This helps the animals know you are a human and not a predator, and it moves you clear of their path should they spook. Horses are prey animals and may be sensitive to potential threats from above them, and may also be confused by people wearing large backpacks. (They also tend to bolt uphill when spooked.) Allow them all to pass, keeping in mind that less-experienced or problem horses are likely to be placed last in line. I also suggest giving the rear of any horse a wide berth. They can't see what you're doing back there, and you don't want to risk a kick.
Generally speaking, right-of-way rules tend to favor the least maneuverable. In this case the 1,000 pound quadruped wins, not just from a maneuverability standpoint but also due to unpredictability (it might spook, bite, kick, or otherwise ignore its rider). In terms of the priority of cyclists vs. hikers, there is occasional animosity between the two groups that may have affected the rules, similar to how many ski resorts heavily restricted snowboarding when it was first starting out.
It's a similar situation here in the UK. We have routes which are designated as Bridleways which Horse-riders, Cyclists and Pedestrians can use but not motorised vehicles.
I would imagine that the yielding to horses is because some horses can get spooked easily and it is safer all round to keep relatively still and let the horse and rider to pass.
Having had horses myself, here in England, part of the reason you give way if you hear a horse coming on a Bridleway is because (and I say this having been in the situation) there is no speed limit for horses on Bridleways (some might have a trot sign but not always), if you're cantering or galloping along which you have every right to do it's harder for us to stop and wait than it is for people to step over. Horses at speed are dangerous to horse, rider and spectator. We giveway to bikers in my area for the same reason, they ring their bell, we move over. Same to joggers. My area in general seems to have an etiquette of slowest mover stops.
I admit that is also incredibly rude to gallop past someone, but there is some historic value to that with UK hunts. Dog and Riders trump people and cars when any form of UK Hunt is being undergone.
On roads, horses are inherently skittish, but not always. Anything from a plastic bag to a lorry's air brake may but not necessarily will set a horse off, which is why in the UK horses on the road trump cars, cars must slow down and pass slowly, emergency vehicles turn off sirens etc. I once even had armed forces slow their march for us as we rode through their land.
Regardless, in the UK as well the rider must make themselves clearly known - high vis is required to walk on our roads, and in general this means you should on a bridleway as well. Part of hacking etiquette around where I am from. In some locations where walkers are common you might also need a license to hack, I've had this in public woodland.
In my experience as both horse rider and hiker, it's best for the hiker to step over and wait, and for the rider, whether of horse or of bike, to slow down (if possible) and say thank you ... you will be surprised how many people don't. For the most part around Buckinghamshire, simply being a walker / biker / outdoors person will put you in a sort of polite and thankful outdoors social circle. Many walkers, and various riders, will say 'Good morning / Afternoon' or 'Hello' to you as you pass, and for the most part they remember to say 'Thank you' as well.
what is the polite way for hikers to behave toward people on horseback?
As for that, you answered it yourself really, be polite. That's all I ever expected as a rider, and it's all I do now as a hiker.