You can definitely bring food into the parks. Glass bottles are not allowed. You can bring a soft sided cooler and rent a locker for it if you don't want to carry it around. We brought a gallon sized ziplock bag loaded with cereal, granola bars, fruit snacks, etc. We had ALOT because we had 10 people eating from that snack bag! The guy checking bags just laughed.
A huge money saver for us was the single serving packets of Kool-Aid. They cost about $2 for 12 packets, and you can get lemonade, Propel, Crystal Light, etc. I brought in a plastic water bottle and filled it up at water fountains. Just add the powder and you are set. You can also get free ice water at any of the counter serve places.
We ended up packing a big cooler in our car and making sandwiches in the parking lot. For about $15 we had sandwiches, chips & drinks for 10 people for two days. Lunch in the park would have cost us at least $180 for those 2 days.