We were there in Jan., in a premium room facing Disneyland. If the fridges are the same in all of the rooms, then I think you can fit a gallon in them (if I remember correctly). I think I removed a small unattached shelf to fit the jug in. I also had to fiddle a bit with the temperature to keep it cold enough but avoid it getting ice crystals in it (though they didn't affect the quality of the milk). You can still fit water bottles or other items of that size in the door as well.
It's a great place! We're excited to be returning in November.