No rolling coolers, but anything that can fit in your stroller or in a locker is welcome. As another poster said, no alcohol and no glass containers (think Snapple bottles) are allowed.
It's not a bad idea to bring your own food. DH and I found that food quality at DL isn't quite as good as it is in WDW. It's not bad and still a cut above other theme parks idea of food, but not up to the level of WDW for the most part (in our opinion).