Hi Stacie,
One of the amenities that I really enjoy when staying at Disney Vacation Club properties is that the villas and studios have kitchens or kitchenettes. Like you, I prefer to prepare some quick snacks and meals in the villa before heading out into the theme parks.
I did some digging on this question, and it looks like most of the studios at Disney Vacation Club resorts have the larger under counter model of refrigerator. One way to check to be sure for the resort that you are staying at is to go to the Disney website for that resort. To do this, go to the
website for Deluxe Villas at Walt Disney World and then choose your resort. Once on the resort page, click on the "Room Rates" tab and then select the deluxe studio accommodation. There will be photos of these studios, which you can then flip through, and in many you can see a photograph of the refrigerator. To be sure of the size of the refrigerator in a deluxe studio at the resort you are staying at, you can call the resort directly using the phone number on the front page of the website for that resort.
I hope that this information helps, Stacie. Have a great vacation, and please do not hesitate to ask if you have any further questions.