Hey there Jimmy,
Welcome to planDisney and thank you for your question! I'm happy to hear that you're planning your next trip to the Happiest Place on Earth.
It can definitely be helpful to bring in your own snacks or water into the parks. However, you'll just want to make sure that your cooler and its contents adhere to the
Park Rules and Regulations list.
According to this page, coolers larger than 24" long x 15" wide x 18" high (61 cm x 38 cm x 46 cm) are not allowed in any theme park. Loose or dry ice is not permitted in these containers. Re-usable ice packs are recommended.
Additionally, glass containers (excluding small containers such as baby food jars) are also prohibited, except in the
Disney Resort hotels.
It does sound like your current cooler's height might exceed the sizing limits. Therefore, it's likely that you would not be allowed to enter the parks with it. My suggestion would be to find a cooler or backpack that fits within the sizing limits on the rules and regulations page to ensure you won't be turned away at the security checkpoint.
Thanks again for your question, Jimmy! I hope you have a fun time on your upcoming trip to the Happiest Place on Earth.
Have a Magical Day,
Greg