That's the tradeoff to bringing a cooler, having to carry it around.
Since the parking garage is covered, the other idea is to leave the cooler in your car, and come back at lunch time around 1pm when the parks are packed.
Another idea, is to bring a water bottle, and some granola snack bars that will fit in your pocket. Yes, you'll save money, but it's kinda hard to do when there are snack stands all over the place.