Summarize:

Although you can't bring in coolers, your best bet on saving money throughout the day is to eat your own food. Pack sandwiches and snacks that you can munch on during your time in the park, so that even if you don't solely eat the food you bring, you won't be so reliant on purchasing food. It is also good to bring plenty of your own water and liquids, as keeping hydrated will keep you less hungry, and purchasing liquids inside the park can be quite expensive. Avoid buying food throughout the day if you're able, especially sugary snacks that will just leave you feeling more hungry afterwards. Set a budget for snacks so that you are forced to avoid spending. Adding a dining plan to your vacation package is a great way to save money on food if you book your vacation through the official Disney site. Doing so can save you up to 20 percent on food over the course of your stay. To find the cheapest options, go to the Vacation Package Guide page. Adjust the "Dining Style" dial to "Counter Service" to filter for the cheaper dining packages. You can also learn all about the available meal plans at http://disneyworld.disney.go.com/planning-guides/in-depth-advice/disney-dining-plan/. Keep in mind that certain items, including alcoholic beverages, are not included in the cost of any dining plan that you purchase. Yes, four sets of Mickey Mouse ears might sound like fun now, but if you're really trying to budget you'll need to cut out spending on everything except for what you absolutely need. Of course, it's totally reasonable to have a budget set aside for certain 'fun' things inside the park, but just know how much you're willing to spend before you start spending. It's easy to feel like something is worth buying in the moment, but later on it's likely that you'll regret your spur of the moment purchase. Look for free pins and items around the park that you can keep as souvenirs. A park map that you mark off along the way may work nicely. Make sure to discuss your budget with your family as best you can prior to entering the park, so as to avoid any possible meltdowns/temper tantrums.
Bring your own food. Add dining to your package on Disney's website. Only spend money on necessities.