Hey there. While it certainly is convenient to have a fridge, it's not technically necessary. I usually get up around the same time as DS, and the most important thing for him to have first thing in the morning is something to drink. So the night before, we go to the food court (on our way back from the parks) and purchase some juice or milk. We then use our ice bucket, and surround the juice milk / bottle with ice. This keeps it good overnight, and then he can have something as soon as he wakes up. If you plan on bringing snack type breakfast foods with you, then you won't have to worry about refrigerating anything, or if you're the type of people who will want to eat breakfast at the food court, then I don't think you need a fridge.
Did that help at all? I feel like I'm rambling.