To read your link though, it says "reasonable" accommodation. It specifies that part of the assessment of reasonable accommodation is if the horse must be house broken.
Can you imagine having a non-housebroken miniature horse in your row with you? I find this hilarious and I hope it happens to me just for the story.
(i)Miniature horses.
(1)Reasonable modifications. A public entity shall make reasonable modifications in policies, practices, or procedures to permit the use of a miniature horse by an individual with a disability if the miniature horse has been individually trained to do work or perform tasks for the benefit of the individual with a disability.
(2)Assessment factors. In determining whether reasonable modifications in policies, practices, or procedures can be made to allow a miniature horse into a specific facility, a public entity shall consider -
(i) The type, size, and weight of the miniature horse and whether the facility can accommodate these features;
(ii) Whether the handler has sufficient control of the miniature horse;
(iii) Whether the miniature horse is housebroken; and
(iv) Whether the miniature horse's presence in a specific facility compromises legitimate safety requirements that are necessary for safe operation.
(3)Other requirements. Paragraphs 35.136(c) through (h) of this section, which apply to service animals, shall also apply to miniature horses.
I got the impression that people were glossing over the details and assuming that it's just an extreme example of airlines being required (if at all--lots of misconceptions abound) to unquestionably accept people's eccentric, ridiculous, and [arguably] illegitimate accommodation requests, such as the recent peacock incident that made the rounds.
Granted, the news reporting has done an exceptionally poor job at distinguishing service animals from therapy animals, and the sources of and justifications for various regulations and policies. But the ambiguity and seeming absurdity is precisely what caused me to dig further and discover that miniature horses are distinguishable. But that only leads to even more questions.
Honestly I have never seen a diaper for a horse.
It's not so much of a diaper, though, and more of a burlap sack that's suspended like a hammock underneath the "business end" as it were.
Note that this only works for poop; I haven't seen any solution for the voluminous amount of pee a horse can produce.
https://www.law.cornell.edu/cfr/text/28/35.136
Dogs and miniature horses--that's it. There's clearly some hidden history and science here. Come on, this is HN! Shouldn't there be several ranchers and at least one legitimate miniature horse service animal owner-operator eager to explain to us the world of miniature horse service animals? What are the relative strengths and weaknesses of miniature horses as compared to dogs? How small can the horses get?
EDIT: The above link is for a regulation regarding government entities; here's the regulation for places of public accommodation: https://www.law.cornell.edu/cfr/text/28/36.302