Have you tried calling the people who gave the class and ask what is ok? Is it just loose ice that is banned. I never put loose ice in my cooler when I go camping. That is a mess. I always freeze my ice inside of a plastic bottle. The larger the better so I usually use an old 1 gallon milk...
When the guy said that you couldn't use ice in the cooler no one in the class asked what is acceptable? Do you have access to electricity at the farmers market? It sounds like you need a cooler with a generator.