No, at DL we don't because we fly and it's too hard to bring things along. Also, it's my vacation and I don't want to try putting together sandwiches in a hotel room. Last year I did try to bring some things, but decided it wasn't worth it (had to pack it all in my suitcase--and I'm talking about a hot pot, French press, coffee, cocoa, and snacks).
However, when we went to Hawaii last year, we had an ice chest in our hotel room and brought food from the farmer's market because the hotel food was outrageous in price and we were quite a long drive from a grocery store. We knew this ahead of time and bought what we wanted before we drove up to the hotel from the airport. It saved us a bundle, so I sure understand where you're coming from. Since there are many options for us at DL, we don't try to bring food.
We like to stay at DLH, too, so I'll tell you one thing that works for us. We like to eat breakfast at Steakhouse 55 at least once. We have 3 little girls (5, 5, and 8). The girls and I split the adult pancake breakfast, which gives each girl a large pancake and 2 for mom. Dad gets an egg breakfast and the cost is very reasonable. We also go right across the way to Compass Bookstore and get milk, fruit, bagels, and that sort of thing. It isn't cheap, though--it costs almost as much as the Steakhouse breakfast! Luckily, my girls and I share a lot. You can also save a ton of money by not getting drinks. Bring your own water and refill the bottle as needed! There are a couple of places in the park to refill with cold, filtered water if you can't stand the taste of the regular water at DL.
Edited: forgot to add that you can have groceries delivered from Von's and...Albertson's, I think. You can choose what you want online and have it delivered, which is neat! I believe you have to be available for delivery within a 2-hour window or something like that. I considered that option since we don't have a car while there, but as I said above, it's my vacation!! LOL.