Actually, a wheeled cooler is one of the few no-nos.I know you can't bring in anything like a cooler but heard you could bring one with wheels. (If you'd like to roll it around all day during the peak season) ... It saves money to buy more souveniers fro WDW.
Last August, we watched security at MGM confiscate a 6 pack of beer out of the cooler belonging to the person in front of us, so I'd say alcohol is a no no!