Have a very similar setup for my airplane. uses ice and water with a heat exchanger, pump and a bilge fan. drawing air through a heat exchanger is the key. I can tell you that I can get about a 20 degree differential from the air coming out of the outlet vs air temp in the heat of the summer, but ice in a standard sized cooler will only last about 3 hours before the water is room temperature. It can knock the edge off of the heat in the cockpit netting an air temp difference of about ten degrees maintained at 90F+ ambient temperature, but only while the cooler has ice in it. then temp quickly begins to rise.
I use it on the ground and during climb out and descent. At cruise it's turned off to conserve the cold. The main reason I use it is because my plane doesn't have Air Conditioning and it can be removed during the winter (the plane has heat) for better payload capacity. Plus it doesn't require any certs.
It would take a VERY large version of this to cool a room. What you would save from your AC bill would go into making ice. you would be better served to use a swamp cooler for a dedicated home operation.
Your use is one of the very few I would think this project would be good for. I was thinking a heat exchanger of sorts would be mandatory in a confined space especially if you did not want to fog up the interior windows. Im guessing that you have a place for the condensate water to go and then pump it back into the ice bucket?