I get where you are headed, but you should probably think about the ice as "fuel." The cost (in terms of heat/energy) of freezing the ice can be spent during times when you are not in the room and/or not using the "air conditioner."
Actually there are commercial HVAC systems that use ice as a coolant - the water is frozen at night when electricity demands are lower and then is used to cool the building during the day.
It was in a dorm and I only really ever slept in the bed. SO I would make the ice in my tiny dorm fridge and put it into the A/C's cooler when I wanted to sleep. This happened only two nights.
