Can small dogs, even toy breeds, be trained service dogs? Yes, they can.
Were the small dogs you saw service dogs, or pets? No way to tell.
The law does not allow questioning the owner regarding their disability. The business is allowed to ask only two questions: Is this animal a service animal? and What service is the animal trained to perform?
They can't ask what the guest's disability is, nor can they ask for any kind of documentation regarding the animal or the animal's training, inquire as to how the animal was trained or who trained it, or ask for the animal to demonstrate its task. If the owner says the animal is trained to perform a service, then the business must give them access under the law. Access can be revoked for the animal (not for the person, just the animal) if it behaves in a disruptive or dangerous manner and the owner is unable to control it. A service dog does NOT need papers or documentation. By law, the business is prohibited from even asking for this. However, there are outfits on the Internet who will send anyone who asks (and usually pays the fee) a service dog certification document, based only on the owner's assertion that the dog is a service animal. Allegedly there is a famous dog trainer that ordered an item like this for his beloved pet, so it could accompany him on airline flights for free. Of course, all he would have needed to do is say the dog was trained to perform a service, but I guess the extra gravitas the document gives is something he wanted.
It is true that therapy, comfort or companion dogs are not considered service animals by law because they are not trained to perform a service. "Having the dog with me keeps me calm" is not a response that would REQUIRE a business to then admit the dog. But the business can do so if it wishes to. There are some states that have passed laws that require companion, therapy or comfort animals to be admitted to housing, but some of the same states would restrict the same animals from food service areas like grocery stores or restaurants.
I believe the law was also revised to specify two types of animal only: dogs, and miniature horses. No cats, rats, birds, ferrets, snakes or iguanas.
There is a list of attractions which do not permit animals, even service animals, to ride or enter. This is due to safety concerns and are mostly the roller coasters, fast rides and others where an animal that could not wear the restraints would be a safety risk. WDW states that a member of the party must wait with the animal. Heard once that
Disneyland is providing some kind of temporary kenneling for owners of service animals who want to go on an attraction where the animal is not permitted.