Couples Negril does have small freezers in the mini-fridge. At least some, and I believe all, of the rooms do. I know this because we (OK, I) put a small tonic water in the freezer to make room for something else, forgot about it, and it exploded later.
I don't recall seeing ice cube trays, but may not have noticed because we use the ice bucket provided in the room to get ice from the ice carts at the stairwell on the first floor of each block.
They don't make ice but one night when we ordered room service we were asked if we needed ice... we hadn't even thought about it but agreed and a large bucket was brought to our room promptly... I am sure if u needed ice a simple call to room service will have it to your room shortly no worries!
They are those little dormitory type fridges so they don't have an ice maker and I suspect ice cube trays have been removed or are hit and miss...I don't recall seeing any in ours though if they had trays it would have the "capacity to make ice". I don't know which resort you are staying at but at CSA there are ice machines on the ground floor of each building.