Hello Barbara! Thank you so much for your question! We always bring a small cooler with us inside of the parks to keep our drinks and snacks nice and cool.
Coolers are permitted inside of Magic Kingdom, EPCOT, and Disney's Hollywood Studios. They are also welcome at Typhoon Lagoon and Blizzard Beach. They are not permitted inside Disney's Animal Kingdom Park (unless it is for medical reasons, in that case, the cooler must be stored in a locker or at Guest Relations).
For safety reasons, coolers must be carried, not rolled or pushed. If it has wheels, it will not be permitted inside of the parks.
You can read about the regulations on Walt Disney World's
FAQ page.
I hope you have a magical vacation! Please come back and see us if you have any more questions!