We don't bring a cooler. For those of you who want to do this, here is what we do:
We freeze water bottles and juice pouches (Capri Sun). Then we make sandwiches out of rolls and whatever (ham, cheese, etc.) We have the sandwiches in ziploc bags. We take Pringles (no-crush!), and maybe cookies (Chips Ahoy, Oreo, whatever). Sometimes, especially if we are planning to spend the whole day there from open to close, we pack snacks like raisins, nuts, fruit (apples or pineapple spears in a ziploc bag), goldfish crackers for the kids (the whole package) etc. All this goes into an empty backpack (or split into two backpacks). The frozen drinks keep the sandwiches cold till lunch, the rolls also travel better then regular bread plus they fill us up more. Everything is disposable and then we have a place to put the souveniers we buy. We do have a stroller with a storage space underneath, so we can store our full backpacks or the empty ones there, but even if we didn't, I believe our method would work. We do not usually take the backpacks on the rides with us as we really need the heat to melt the drinks. We leave them in the stroller. If you are all adults, each one could carry their stuff in their own bags or combine into one sack and take turns carrying it full.
Also, we carry very, very little else into the parks. I find some people carry way to much stuff in general. We have a camera, wallet, keys, and a change of clothes for the baby (she's potty training, so no diaper). When she was younger, I carried the change of clothes and about four diapers and a wipey thing. That's it. If you fall anf get a cut, scrape, etc. or if you need Advil, Tylenol, whatever, go to First Aid. It's free. We sunscreen up in the morning, and sometimes I may carry a travel size sunscreen for may very fair skinned kids, but the rest of us don't need it. Anything else is not necessary IMO.