It's called evaporative cooling, and until recently the principle was the way the vast majority of Arizonans cooled their houses. (They are called swamp coolers down there.)
It only works in dry climates, but it makes such a difference.
Yeah, I'm from FL. Swamp coolers don't work most days. Just makes ya wetter. I was in Az a couple months ago and it was pretty neat figuring out that sweat truly does work.
Also - it only works for part of the summer; we're in our so-called "monsoon season" right now, and humidity is highly variable, but is generally above what most evap coolers will help with.
However, if there is some evaporation that can takes place (that is, the evap gradient is large enough to let it happen, but directly using that cooler air would make it uncomfortably humid), you can instead do what is called "evaporative chilling" (or something like that), where you run the water over a radiator, and the water evaporates, cooling the radiator (actually, removing the heat), and inside the radiator, you run coolant/water mix - that's your outdoor side. Inside you have another radiator, with a fan circulating air over it. It's something like an A/C system, with water/coolant as the "working fluid" and no compressor, just a pump. Think of it like a "dry evaporative cooler".
This kind of system does work - it's actually used for industrial A/C systems as some kind of "pre-chiller" or something, but it isn't something you can buy for a home that I know of - but you can build it. But like all evap systems, once the humidity gets too high, it stops working.
Another kind of system that can be used here in Arizona, but few do because it is ugly, big, and works only so well - are something called "solar chimneys".
The simplest is just a large 2-3 story structure painted mostly white at the bottom and mostly black toward the top; the idea is that the sun warms it, sucking air thru it and out the top - the bottom end is connected to the house, to make a "forced draft" through the house.
The better way is to make a similar "chimney" on the opposite side of the house and add cooling pads and a fan at the top (basically a large diy swamp cooler). Misting can also be used. So you evap cool the air, which falls, enters the house, then is sucked up and out the other side by the "hot" chimney.
Another "hot climate" design for cooling is something that used to be found all over the middle east:
As you can see, this is basically the ancient form of "solar chimneys" - if we instead used these in Arizona, coupled with either monolithic dome construction and/or rammed earth, and below-grade construction (to take advantage of earth insulation and cooling) - it'd be so much better for energy use here in Arizona.
Oh, this irritated me so much growing up in Tucson. I would read about something like passive water heating, or all of the ways we could reduce our need for AC (even back growing up where climate change was more theoretical) and saw that people didn't care.
It only works in dry climates, but it makes such a difference.