yes you can. they have certain restrictions such as no alcohol, glass (excluding baby food jars), no straws at AK for safety of animals, coolers larger than 24'' long x15'' wide x 18'' high.
we typically brought a collapsible lunch bag with a frozen water to keep things like sandwiches cool (then drank it), chip type snacks. We just watch for things that melt like chocolate (or ate it earlier in the day).