Service Horses vs Service Dogs
The services horses shown above are all used for help, not as pets. Mini Horses are allowed most public places, but some places do not want horses to be inside of their businesses, and it could be a hazard to certain people, as some people are allergic to horses. If a public place doesn't allow the service horse, they would either wait outside for their companion or wait in the car.
Service dogs are also meant specifically for helping the disabled. Service dogs are allowed in almost every public venue. You are not allowed to pet or touch service dogs while they are working.