How can you cool house with well water?

You have to do it by recirculating the water, or basically letting the water drain back into the ground somehow. It will only work if you have your own well, and live on a large acreage lot, and not by hookup to city water system. Here's how:

You take water from the well, usually at around 55-60 degrees F and pump it through a radiant system made up of a series of radiator-style cooling tubes, which can be metal or plastic (better since metal can rust/corrode more easily and plastic radiators are common now). The water then must go into a underground "cistern" of a sort that will allow it to seep back into the water table. Something like a septic tank leach field but without the septic part. If you just let it seep into the ground at yard level, that will work, but you better have it on a wide drip system, or you'll get puddling and also too much vegetation to constantly cut.

So then the other part is to circulate air over the cooling tubes and into the home. A re-circulating system like a furnace blower would do it. Your home would typically be kept at around 70-75 using kind of this system, if it were set up properly. Another advantage is that it will keep your home above freezing in the winter without using a heater, like if you are away for a while, since the underground water temp is always 55-60 degrees.