They will provide a free refrigerator if there is a medical need for one. Generally, they are talking about medication, so the refrigerator doesn't need to be very large.
The type of refrigerator they provide depends on what they have available. You could get a small, dorm type refrigerator or one that is roughly the size of a shoe box.
If he has food that is medically necessary and needs refrigeration, I would certainly mention that.
An alternative that a lot of people have used (other than renting a frig) is to get a cooler (collapsable ones can travel collapsed in your suitcase). Once you get to the resort, you can get a ready supply of ice for free. Have plastic bags to contain the ice or hold the food so it doesn't have contact with the water. Many people have posted that replenishing their ice twice a day keeps things quite cool.