I took my family to Sea World last year and brought in a cooloer everyday! My DS has a peanut allergy and needed to eat things that I knew where 100% safe. I put the small sided cooler in my DH backback and no one asked about it. I did call before and was told if anyone at security said anything to ask to speak with someone at guest relations and that they would take care of it. But no one ever said anything to us!!
Hope that helps and have a great time we just love Sea World!
I'm a SeaWorld annual pass holder and have visited two times recently (May, July) and have always brought a small, soft sided cooler. Just the usual rules, no glass, alcohol, etc. The cooler never raised an eyebrow. Definitely bring water with you - it's sooo expensive in the park!