Technically speaking, the ADA applies to both dogs and miniature horses. Not sure what the rationale for horses is, but they’re expressly permitted by the ADA.
A blind student at my undergrad had a miniature horse seeing eye horse. It was always quite a sight on campus 
Believe it or not there are guide horses for the blind.
Guide horses are little, about the size of a large dog. Horses live longer than dogs, so a blind person wouldn’t have to face the loss of their guide animal so soon. Horses are prey animals, whose natural caution can be a good fit for a blind person needing a safe guide in a crowded chaotic area. Or so the guide horse web page says, anyway.
We saw a miniature guide horse board the parking lot tram at Disney World 2 weeks ago!