Are assistance dogs allowed in the park?
Yes.
The ADA (Americans with Disabilities Act) requires that Service (Assistance Dogs) be allowed pretty much where ever the owner needs them to go. The ADA does not give the same protection to 'Emotional Support Animals.'
Quite a few regular posters to this board do use Service Animals and I'm sure will chime in with help. Until then, here's some stuff to get you started.
There are some attractions that Service Animals are not allowed on. This is for the safety of you, your dog and the other guests. Generally those are rides where the dog might have some problems with, no matter how well trained; such as in the air with no restraint - like Soarin' or Peter Pan's Flight or lights/sounds that would be uncomfortable for the dog.
For those attractions, someone in your party will need to stay with the dog during the time the rest of your party is on the attraction.
You can find more information if you go to the disABILITIES FAQs thread (near the top of this board, or there is a link in my signature). In post #3 of that thread, there are links at the top of that post to the Guidebook for Guests with Disabilities for each park. Those Guidebooks include information about which attractions Service Animals are not allowed on.
Further down on that same post, there are some links to different conditions/situations. You will find a number of links about Service Animals.