Sure it's allowed, and you won't look rediculous. Most people who see you will be thinking, "Darn, why didn't we do that?"
On a recent visit, we had 3 coolers. Two that we're holding drinks, and the other was holding doughnuts with a dry cool pack. Stuff gets waterlogged if it sits on the ice. Saved leftovers from a restaurant, and had them the next evening at home. Milk and doughnuts for breakfast are a great idea, because you can get an early start without having to visit a restaurant.