You can bring in small cooler.....but if it os for water then you may not need cooler as they have good fountains with good quality of water......also you can aak to any restaurant for providing cup of water and they will give it to you free of cost.......as much as low your belongings you enjoy more.
You are allowed to bring in a cooler. Suitcases, coolers or backpacks with or without wheels larger than 24" (61 cm) long x 15" (38 cm) wide x 18" (46 cm) high are not permitted in the parks. (Coolers required for medication may be stored in a locker or at Guest Relations.) So, as long as your cooler is smaller than 24" X 15" X 18", you'll be fine bringing it with you. Most soft-sided coolers that I've seen fit within those dimensions. You are not allowed to bring in wagons of any sort.
I don't know about a cooler. I haven't tried that. I am sure you can bring in a small one to fit in a locker. I have seen people with wagons.
Thanks! Your answer is awaiting moderation.