Hi Connie,
Welcome to the Moms Panel!
You are welcome to bring a cooler for your snacks & drinks as long as it is not larger than 24" long x 15" wide x 18" high.
There is a link on the Disney website that lists items that may not be brought into the parks - click
here.
You are also more than welcome to bring drinks and snacks inside the parks - we do every trip. There are a couple of exceptions to this - no glass containers (except baby food jars) & no alcoholic beverages.
I always bring a couple of Ziploc baggies with me. They are great to have on hand in case you have some leftover carrots, grapes or other non-perishables from a meal that you can save to snack on later.
You will have to open all of your bags (purses, diaper bags, coolers, camera bags, etc.) when you go through security at the theme parks. Be sure you go ahead and have everything unzipped, opened and ready for inspection. That will speed up the process and get you into the parks faster.
Let us know if you have additional questions. We're super happy to assist you!
Wishing you many magical memories :-) Allison