I think once? A really long time ago. I have a vague memory anyway. It might have been a pony instead of a "horse" horse.
No.
Maybe? I'd have to ask my older family members. If I did, it was when I was really little.
There's a fenced field in the NE part of town that has horses near the sidewalk. If they're out, sometimes I'll give them something to munch on if I have something to offer when I walk by. It's been a while since I've been in that area, though... oh, I think I have a picture:
https://gamefaqs.gamespot.com/a/forum/e/e9ab04ef.jpg
I took that photo years ago, but horses can live a long time, so I wonder if this one's still there.