Can it be done, absolutely, and it is done in commercial buildings and schools every day, chilled water flowing thru a coil picks up heat from the air being moved across the coil, and cools the room.
Ain't no big trick to accomplish, unless you want to get into serious efficiency. The amount of thermal transferr that can happen as the air passes the coil becomes the fly in the ointment, and a car radiator ain't gonna cut it. If you gang about 5 radiators behind one another in the air stream you can get efficiency. A second problem in any coil/airstream aplication is how you move the air across the coil. Blowing air across a coil requires equilization difusers, or you get a hot spot in front of the fan, and a lot of unused coil. If you **** the air thru the coil you get more or less equal flow and maximum transferr.
You also need to understand that air passing a coil can only cool so much with each pass. The long and short of this is that you either have a very cold coil to acheive maximum cooling, or you keep running the same air thru the coil acheiving a little temperature loss with each pass.
If you go with the constant air movement plan, you need to control the water flow rate thru the coil so you aren't wasting a lot of water. Fortunately, this isn't too difficult to do with a thermal sensor and a valve, you can even computerize it if you want to really have fun. Ideally, you'd want the exhaust water to be only a few degrees colder than the ambient room temperature, given the propertys of liquid coils and airstreams. This would minimize water consumption as well.
What to do with the spent exhaust water, well, there is always drip irrigation with a spent water tank. That way you don't need to spend a lot of money on pumping water. If you happen to have a flowing creek next to the room you're trying to cool, you are way ahead of the game, presuming you can filter the incoming water so it doesn't plug your coil. Creek water will generally be at a lower temperature than ambient air temperature. Keep your mouth shut about the operation though, or some tree hugger will get DEC on your A$$ about thermally poluting the creek.
Removing humidity from the air, as long as the air side of thecoil is at a few degrees lower temperature than the dew point of the ambient airstream, the coil will condense humidity out of the airstream. Of course you also need to factor in either keeping the air stream speed slow enough to allow the condensation to fall off the coil, or you can't drop a whole lot of humidity out of the air stream. This can be overcome with a trick or two.
As far as ground loops and using black plastic pipe, forget it, standard poly pipe ***** as a thermal conductor.
The best coil units are either the coils used as room boosters in duct systems, or fairly decent sized air conditioner condensers. You need to do a bit of modifing on most AC condensers if you can even get them before the scrap guy does these days.
Just in case you're wondering, I do live next to a flowing creek, and the DEC possum police are real azzholes. Fortunately, I am allowed to pump water for irrigation purposes.
All the above said, you'll keep your workspace a lot cooler by just employing Mother Nature's free air conditioning. Every night after the sun goes down, she lets you pump all the accumulated heat out of the atic space and insulation with a very small fan at minimal cost. Use a clock to control the fan, and you're fairly comfortable for cheap money. Install a louver into the atic space and **** cold air in just above the shop floor, and employ that floor as a thermal battery to keep the room cooler during the next sun cycle.