To re-iterate some of the things said by SDMB ninjas
Human have domesticated horses, dog and cats for a very long time. By some selective process, deliberate or incidental, we’ve manipulated their behavior to suit tasks for human benefit.
I bring up cats because people sometimes claim that they’re “not domesticated” or “barely domesticated” or “they domesticated us, har har.” Sigh Cat’s are domesticated, in that unlike tamed wild animals, they are very unlikely to attack us at random. Cats seem to not be domesticated, because the behaviors they exhibit are the ones we want – a certain aloofness, skulking about searching for vermin, etc. Another thing – genetically, there’s not much “raw material” for a wide variety of behaviors in cats. The proto-domestciated cat may simply not have had much to work with – its a small, vermin eating carnivore, that’s it. That’s all it has to do, and it can’t really do much else. Likewise, horses have been bred for working tasks. There may not be much “room” in the gene pool for other behaviors. Or we just may not want any sort of behavior from a 1200 lb animal besides stability.
Humans spent a great deal of time domesticating dogs. And we’ve gotten a certain “surrogate pack” concept bred into dogs. Dogs almost have to project enthusiasm at every mundane aspect of their lives – reaffirming that they’re part of the pack. There are humans who do that too – we call then attention seekers. Its wrong to apply that to a dog, because its just doing what it can with the behaviors we’ve left encoded. But its equally wrong to say cats are “aloof” and horses are “disinterested.” It makes about as much sense to apply those to animals as it would be to ask one for help with your taxes.
Horses are herbivores. Their job, in a sense, is to eat and eat and eat as much plant material as possible, to maintain life processes and maybe lay down some fat for leaner times. This takes lots of time (not as much as cattle, horses aren’t ruminants) and yeah, they’d probably like to stay in the stall, and eat. Dogs, and more so, cats, are carnivores. A little bit of meat and maybe some vegetable matter for dogs, and they’re good to go, up for an adventure or whatever.
Horses are also herd animals. We’ve manipulated their herding instinct to see humans as part of the herd. Horses don’t do well in isolation, locked in a stall, they can develop all sorts of bad behaviors: chewing the stall boards, kicking the walls, biting the stall boards and sucking in air – that’s a bad one, really causes stomach problems. So yeah, a chance to be out, in a herd of humans, is probably relished.
Also, you may be misinterpreting behaviors. Lots of dogs like to play. The dogs guarding the airport or guiding the blind don’t seem to want to play with me much, seems like they have their pack work to do, and don’t care much for me. The horse may well be worried about you, a stranger, on their back – that’s where predators go. Or it could be focusing on the trail ahead, keeping you safe, given that its obvious to the horse that you have no idea where you are or what you’re doing – you probably wouldn’t be able to outrun a mountain lion, and your kicks won’t likely kill one.
Or the horse could just be focusing the scent trail of the filly up ahead.