We are here right now and I have actually seen many coolers. At the fireworks the other night, we were standing next to a family that was dragging around one of those collapsable coolers on wheels. They had two more bags sitting on top of it. Looked more like they were headed for the airport rather than a theme park.
And that said, I entered everyday the first part of this week with a backpack bulging with water bottles (5 kids & 3 adults in our group). They just smile and say thanks and wave me through when I open the backpack at security. But I must say, that backpack became a pain - to store at the crowded lockers and to just haul around. So, now I shell out the extra money for the ice cold waters in the ice bins. They are 2 for $4.00 and with the AP discount, they are 2 for 3.20. Well worth it not to have to fight the crowds at the lockers on certain rides!