Hi Chris:
You can mail yourself a package containing anything you might need during your stay.
The mailing address of All Star Sports is:
Disney's All-Star Sports Resort
1701 West Buena Vista Drive
Lake Buena Vista, Florida 32830-8401
(407) 939-5000
Most people tend to arrange for their packages to arrive a few days prior to their stay. I would be concerned that a package that arrives many weeks prior to a stay may be misplaced. To make sure your package doesn't arrive too long before your stay, or after your arrival, you should speak with your shipping service to find out when to mail the package so that it arrives a day or so before your arrival. On the package, write your name, note that you are a "guest," and include the date of your arrival. Although probably belts and suspenders, I suggest also writing a note on the package saying "hold for arrival."
When you check in, ask for your package. I would bring confirmation numbers from your shipper just in case the package needs to be traced for some reason.
I'm not sure what snacks you have in mind, but items such as cereal and energy bars will likely transport well. Food that my spoil, leak, smell, or otherwise make the package look suspicious may cause the package to be discarded.
Enjoy your vacation.