Since my 7yo is diabetic, we must carry quite a bit of "stuff" with us all the time--medical supplies, insulin, fast-acting snacks. So when we went to WDW 12/5-12/11, we carried a backpack full of stuff. We were able to take it with us on
every ride (Space Mountain, Rock n Roller Coaster, Expedition Everest, Mission: Space, Soarin', Kali River Rapids) with no problem. Where there was no storage provided, we put the bag between our feet.
Your bags will be checked before entering the parks. Coolers and large bags are not permitted in the parks. I never saw them turn anyone away for carrying in food in small quantities, though.
One word of warning--unless there is a necessity for what you're carrying, remember that bags get heavy after all day at the park, and, unlike children,
MUST be carried all the time
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