Officially, you're not allowed to bring these in. This is from the UO website:
Security Procedures
For your safety we have increased security procedures and ask for your understanding and cooperation.
Coolers are not permitted in the Parks.
No outside food or drinks may be brought in.
All bags, backpacks or packages will be inspected prior to entering our Parks.
We recommend you leave unnecessary articles in your car and secure valuables in your trunk.
The following items are not permitted: any type of weapon, alcoholic beverages, illegal drugs, large duffle bags, folding chairs and large umbrellas.
All that being said, we always bring in cooler bottles that we bought at Wal-Mart. They're one liter bottles that zip into an insulated cooler wrap. We always fill them with Gatorade and either freeze them (if we're staying somewhere with a full size refrigerator/freezer) or load them up with ice. We usually use the powdered Gatorade so it can be made strong for when the ice begins to melt. Need to replace those electrolytes in the Florida heat or I get like this
We usually also bring along granola bars or some small non-melting snack item that fits in a pocket or fanny pack. Although all bags are checked when you enter the front gates, we've never been told we couldn't bring these things in with us.
Hope this helps.