What a magical vacation it will be to see Walt Disney World Resort through the eyes of your 3 year old. I'm so excited for you Brigid!
You absolutely can bring snacks into the theme parks. There are just a few
rules you will want to be aware of. Glass containers are not permitted (excluding small containers such as a baby food jar). There are size limits on coolers though I would imagine you will just be carrying the snacks in you backpack or bag.
When our kiddos were younger, we always packed snacks and typically, packed too many. Several times the snacks ended up as crumbs. After several trips of cereal that crumbled to powder, we divided the snacks into individual sized servings and placed them in plastic snack bags. The snack bags were placed in a plastic pencil/supply case. The pencil case was the perfect size to carry several snacks and the snacks fared better with the plastic case protecting them. I also packed additional empty bags to easily carry any leftovers we had at meals that my little ones might want to enjoy later and could safely be carried through the theme parks for several hours without needing to be refrigerated.
The snacks we took with us were always appreciated but our kiddos loved the delicious Walt Disney World Resort snacks. One of our favorite memories/photos is of our son when he was 3. At his request, we bought him a chocolate chip cookie from
Les Halles Boulangerie-Patisserie in the France Pavilion at Epcot. I truly believe the cookie was the size of his head. He was ecstatic. (And then the empty plastic storage bags came in handy as we were able to place what was uneaten of the cookie in a bag and take it back to our Resort hotel.) Who knew a simple chocolate chip cookie could bring so much joy? Disney magic!