Hi Sonia,
There are very few rules about bringing food items into the Disney theme parks. The only restriction is that you can not bring alcoholic beverages into the parks and you can not bring in glass containers other than baby food jars. Everything else is perfectly permissible. You're welcome to bring snacks, soda, water, milk, juice, fruit, sandwiches, etc. I always brought crackers and juice boxes into the parks with me when my kids were preschoolers.
There are security checkpoints at the parks, but they are looking for safety issues, not food.
You should be aware that while any food is fine to bring to the parks, there are limits on the size
cooler you can bring with you. The rule is that you are not permitted to bring:
Suitcases, coolers or backpacks with or without wheels larger than 24"
(61 cm) long x 15" (38 cm) wide x 18" (46 cm) high. (Coolers required
for medication may be stored in a locker or at Guest Relations.)
As long as your cooler is smaller than this, then you're good to go.
Have a great visit to Walt Disney World.