Hi Jason!
To answer your question, yes, you can bring outside food into the Disney Resort hotels, and you can bring snacks into the theme parks. If the room you have reserved does not have a refrigerator, you can rent one from most of the Disney Resorts for a small fee. Also, be sure that any coolers or backpacks you take into the parks do not have wheels on them.
We always keep snacks that can double as meals in our rooms - things such as peanut butter and bread, breakfast bars, fruit, and drinks. When we are not on the Disney Dining Plan, we eat in our room often, especially for breakfast and late night snacks.
I would like to share with you, however, that at this very moment Disney is offering a special vacation package for select arrival dates in October 2011 through March 2012 that includes a FREE dining plan. I'm not sure if you are able to change your plans or revise your reservations at this time, but it might be worth investigating. You can learn more about this plan by clicking
HERE.
I hope you all have a very fun and memorable vacation in Walt Disney World!