Groundwater cooled heat exchanger - forced air
Using only cold water to lower a buildings temperature was common many years ago. I have not seen any of the systems that still work but I do know  or was told that they worked. This would be similar to a typical A/C system except that the cooling medium would be water instead of a refrigerant cooling the air.  Know this that most large buildings, schools, hospitals, and office buildings use cooled water to do the A/C since it is easier to circulate a cooled water than to have spot cooling everywhere. In your case, instead of using a refrigerant to cool the water, you will use a dedicated cold water source as your cooling medium. A cold water source is located, a well, an underground stream, or an aquifer that is tapped into and the cold water was pumped into a water coil similar to an A/C coil and the discharge water, now slightly heated is returned back into the source. This idea will work if the source water is cold enough, you can remove and return enough water to suit your needs, and it is allowed by the codes concerning this action. Will your idea work, yes, is it allowed, ?, is it cost effective, I do not know.