Dogs have no concept of society beyond the pack that is family. Dogs prefer to communicate by action and smell. Maybee antromorphizing makes alien company more bearable. I somehow miss that trait, i guess.
Pretty sure, yeah. It's an extrapolation: my dogs don't try to eat another dog that's about the same size and furriness of a rabbit, but they'll about take my arm off to chase a rabbit. So there's some kind of categorization going on. "These things are for eating, these other things are for fun." I'm quite confident that dogs have not created a system that breaks things down along lines of genus and species, but I'm pretty sure they know I'm not one of them. To a large degree it's moot, I suppose, because they can't tell us what's on their mind, so we just have to play with inputs and observed behavior, and go from there.
As a sidenote, research has on multiple occasions demonstrated that pack mentality and other such things as "alpha dog" don't apply to domesticated dogs (IOW, you can pretty much ignore anything Caeser Millan has to say). Extrapolating from those assumptions can be rife with error.
I can't speak for horses because I have little desire to be around them, but it would take some solid evidence to convince me that a dog doesn't know the difference between humans and dogs. Perhaps a dog doesn't bucket me into "human" or "dog" (though I'm confident that they have some concept of categorization), but they sure heck don't think I'm a bipedal dog.
As for "horse people", well, I make no apologies for that lot. I think there's something in horse dander that makes the owners neurotic.