Not sure about a cooler, but a bag with snacks or sandwiches should be accepted. We brought something similar ourselves.
I had children with me and a diabetic, they allowed my nap sack with snacks and juice boxes. They were more concerned about not feeding the animals human foods and littering though.
You can take your food from home. Large bags are allowed, just show them to checkers
Yes, from experience last weekend, one of my family brought in a small insulated lunchbox with her food in it. I'd bet a large cooler would be pushing it.
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