Service dogs are not required to wear vests. However, service dogs also are usually trained to be passive and do not approach and bite people. at any rate, anyone can purchase a vest online and slap it on their pet. If a service dog bites someone it could be removed from the park.
Not sure what Disney's current policy is on the admission of emotional support animals, which are untrained pets whose presence is prescribed by a health care provider to assist the owner with a mental health condition. ADA does not require a business to admit emotional support animals, but one may do so if it wishes.
In Florida, it is a misdemeanor to pass off your untrained pet as a service animal.