If you can squeeze it in a small backback, you should be able to bring it into the park. Don't try to drag a cooler full of picnic stuff behind you thru the checkpoint. I think they would flag you for that...
We always bring a few snacks with us when we go to the parks. Usually a couple of bottles of water and something to munch on, nothing too elaborate.
Remember that the "company line" is no outside food or drink so don't be upset if you get flagged.
Have fun!!!!
Sunking