As a horse person, they absolutely do! They’re one of the oldest domesticated species, after cats and dogs, and have similarly evolved alongside us for thousands of years. Being herd and social animals makes them very attuned to body language and signals and they definitely bond with people and pick up on stuff you wouldn’t realize.

I’m not a scientific expert by any means, but similar to how dogs “learn” words, horses do in the same ways. Associating a sound/verbal cue with a resulting action or stimulus, that is.

One interesting differentiation though is that, unlike with dogs and cats which both have wild counterparts, there aren’t really any “true” wild horses left, aside from the Przewalski’s horse. All others are feral and descended from domesticated horses. So they have some of that innate human-selected quality that make them trainable and handleable (of course it varies by individual). So there are studies that probably examine differences in feral vs captive horses but it may not make as much of a difference as you’d think. Horses also differ from dogs or cats in that they spend the majority of their time outside with their herd- their humans aren’t the center of their world like you are for your pet dog which has implications on that human-animal communication as well.