I went to law school with a woman who had a service miniature horse. It was able to give her more physical/balance support than a dog. It was about the size of a large dog but a bit stockier. It was never a problem in the hallway or in classes or anything and didn't smell.

The only time it was an issue was in the ladies room. The bathrooms were ADA compliant, at least in theory, but small. There were three stalls total - 2 "standard" and 1 wheelchair accessible - but a woman + a horse are a bit wider than a wheelchair and the horse wasn't quite as agile a dog and couldn't maneuver well in the small space.

I regret that I didn't ask her where she kept the horse in Boston - did it live in her apartment? Outside? No idea how that would work.

can these horses be trained not to poop and pee indiscriminately?

The article's last sentence says that training is still required, so in order for this news to have any effect with respect to service horses on planes, the answer to your question is impliedly a yes.

Horse diapers (manure catcher) seem like the obvious solution here.

Nothing like flying next to a horse with a diaper that’s been filling up for the past two hours.

Herbivore poop doesn't stink anywhere near as bad as omnivore/carnivore poop - yes horse/cow poop stinks, but so little compared to cat/dog poop it doesn't even register on a scale.

Sounds like you'd gladly switch seats with me on a 4 hour flight next to a horse.