One drink per person and one snack per person. Yes, they have free ice water as much as you want any stand that has soda machine. small cooler may be brought in only for baby bottles or diabetics that have to refrigerate their insulin.
In addition to the other responses, you can also purchase the souvineer mug and bring that back in for discounted drinks in the park. Not a bad idea if you plan more than a day there!
They let us bring in water bottles/camelback in a bookbag...but no coolers
I don't really know but they do have free ice water
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