Hi Linette,
Love to see that you are planning ahead!
You are welcome to bring a cooler into the parks as long as it is not larger than 24" long x 15" wide x 18" high. Unfortunately, wagons are not allowed in the theme parks. There is a link on the Disney website that lists items that may not be brought into the parks - click
here.
You are more than welcome to bring food & drinks inside the park. There are a couple of exceptions to this - no glass containers (except baby food jars) & no alcoholic beverages.
There are
lockers available for rent where you could store your cooler and not keep up with it all day at all four of the theme parks, Downtown Disney and both water parks. Click
here for more information on locker sizes.
If you are visiting Disney's Animal Kingdom park, you will not be permitted to bring in balloons, straws and drink lids as they are a safety hazard to the animals.
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 park faster.
Wishing you many magical memories :-) Allison