Not a know it all but,
Not all Carnival ships have fridges. Only the newer ones. And those act as mini-bars in which you have to ask for the key from the Steward and agree about paying for the contents.
And as Rick said they keep your ice going. I might suggest bringing a small cooler as well. I do for my beer, and they keep it iced for me.
If you do get a fridge, nicely ask the Steward if you could put a few small items in it if you feel better than the using the ice. A few is all would fit as it is already packed. I would use the ice though, the fridges are not that cold.
The fridge is not a cabin amenity for use. It is a mini Carnival Store of Soda, Beer, Goodies, and Liqour. They have every right and reason to not make it available for your personal cold storage.
Hope this sheds some light on the frig in your room question. For some odd reason I think I answered the wrong question