Unless you attempt to drag in a full-size cooler packed with a week's worth of groceries, Disney actually does not frown upon guests bringing in their own food and drinks. You can save a ton of cash by packing water (don't forget your reusable bottle!), a few snacks, and maybe even some sandwiches to hold you over until that special meal you booked.
Disney doesn't permit loose ice or glass containers, but most food and drink items are fair game. We're not saying you shouldn't partake in Disney's many, many delectable treats, but mixing in a few of your own will be much easier on your wallet.