I had no problem getting a refrigerator, which they didn’t even charge for. (They usually do, but when they heard it was for diabetes, they didn’t charge.)
Most restaurants had sugar free desserts available. Some of my breakfast places had those little boxes of cereal, so I tended to grab one or two to keep with me for snacks.
These great places on the web have lots of suggestions on how to make your Disney vacation with diabetes even easier:
Disney World for Diabetics
Disney with Type 1 diabetes
DLife’s Disney with Diabetes