There is two horses, sure, but I can fully understand someone writing: There's two horses. It might be grammatically incorrect, but that's how people speak. It is where I come from, anyway. And of course, I'm only referring to dialogue here, not narrative. But even then there are exceptions. If you're writing in first-person and using a distinct 'layman' style, you'd probably use the example in the narrative too.
I've laboured over a few of my choices in the narratives of my typical First Person 'layman' style pieces. I treat the narrative just like any dialogue passage. Contractions, grammar slips and all. My Northern Irish slurry truck driver doesn't speak the Queen's English. (Doesn't pay heed to style guides either, for that matter. )
Exactly! In fact, I'd go so far as to say that in first-person the narrative must reflect the dialogue (or at least the dialogue of the storyteller). Else you would have this: I looked him directly in the eye. "Piss off, arse'ole, or I'm gonna rip your head off and piss down your neck!" The gentleman looked back at me and appeared to be very angry at my comments. I realise now that they were very unwise words, but at the time I was hopping mad and simply couldn't control myself. It was a foolish bravado and one to which my bruises can attest. The only context in which the above can work is if the narrator is a very well-spoken man who was pretending to be a tough, working class bloke.
Sure, and I think I've said here (or meant to) that all bets are off when we're talking about dialogue or dialect, and I'd include first-person narrative as dialect in cases like you're referring to.