There are many reasons why you can't just circulate cold water though a radiator to cool. As another commenter stated you will get large amounts of condensation. But the other reason is that you do not get nearly as effective of convection currents with cool versus heating. Your radiators utilize convection currents to circulate the warm air around the room. Running chilled water though the a radiator would be like having an ice cube in the corner of the room. It isn't going to cool the whole room down and will get water everywhere.
