We were there end of April and
everyone was bringing in food. We brought two small soft-sided coolers. I saw one man with a rolling cooler. We went back to hotels for dinner but brought drinks and snacks back for all the night shows at the parks (popped popcorn in the hotel micro and brought it). We had water bottles every day.
They seemed to not care at all as long as you opened your cooler and let them inspect it. Bringing in food is a very good way to keep your little ones happy! I bought Disney-themed cereal, fruit gums, etc at
Walmart and packed them for the kids. They were perfectly happy with that, plus we bought one 'treat' each day (sundae at Mrs. Potts, for example).