I saw it a few times when I lived in New Mexico. I think it was in Corrales, NM. Also, when I was doing the 2010 U.S. Census, some of the census takers went out on horseback to the more remote pueblos.
I will never let you part, for you are always in my heart: MJ
turn to page 394: Snape (nasty woman)

I haven't seen that but quite a few years back I saw a teenage girl in the drive thru line with a dog on the leash. At least she was being thoughtful not to just tie dog up outside. We were behind her so had to move up a bit to activate the sensors. The worker seemed a bit confused at first that the car was then giving another order but it worked out well.
I once saw a TV program featuring McDonalds in various places. One has a drive thru window for snowmobiles.

Yes. Here in Texas, you can go through the Whataburger drive-thru on horseback.
Two weeks ago, while visiting my in-laws in a small south Texas town, we saw a riderless horse strolling through the parking lot of the restaurant where we were having lunch.