The gift shop at the nearby Saratoga Springs resort includes a mini convenience store. This is about a 5-7 minute walk from most of the treehouses, or you could take the internal Saratoga Springs bus (which would likely take longer).
The selection is not large, but you will find some basics like milk,
juice, eggs, bananas, cereal, dry pasta, canned soup, a loaf of bread, sliced
cheese, soda, etc. For my family's tastes, I'd be able to find
the makings of a basic breakfast or lunch there, but for dinner I'd
need another source of supplies.
To get fresh meat or veggies, you would need to rent a car or take a
cab if you wanted to visit a grocery store. Another popular alternative
is to arrange for a grocery delivery. You can read more about this
HERE.
Have a great trip to WDW!