[jeff5may]

Q: What is a heat pump that's not a heat pump?
A: A cold pump.

You can build all manner of the type of coolers like you are considering. A simple example is to use well or tap water which has been cooled to underground temperature and run it through a forced-air radiator to cool the air. The outlet water can be dumped to wherever you want. These type of units are good at reducing the "sensible" heat but not very good at removing the "latent" heat in your area to be cooled.

What this means is that they will cool dry air well, but as the humidity rises, they lose effectiveness. On hot, humid days, they make the air "clammy" rather than "steamy". The water vapor stays in the air because it cannot condense on the radiator.

Also, as the difference in temperature between your indoor air and your incoming water gets small, they become less effective. I.E. Ice cold water grabs more heat from the air than cool water, or, A hot room has more heat to grab than a warm room. Either way, when the ice water warms up or the room cools off, your radiator has to work harder and longer to move heat.