Joseff and Tom Hockley are right: when a liquid evaporates, it needs to take heat from the enviroment to gasify. That's the reason why you feel cold when you put cologne on: the cologne robs heat from your skin to evaporate.
This is the way all refrigerators and freezers work: by compressing a gas, converting it to a liquid (and producing heat in the process, heat that radiates in a radiator at the back of the freezer) and then allowing it to expand into a gas at a valve. When the liquid expands to gas, the pipe gets cold because of the heat that the liquid needs to adsorb for the phase change to occur.
The expansion takes place at the valve marked "C":
Now, there are many autos with air conditioning: it works in the same way.
The problem to use it as a cooler, instead of water, is the added weight of the compressor, plus
the hefty power you need for the compressor to work and liquify the gas, not because the gas weights much more than water (it weighs more or less the same). Of course, a water pump also weighs, but the power needed to impulse the water is much less than the power needed to convert a gas into a liquid.
Besides, as I explained, when you re-convert the gas to liquid, you generate heat (the inverse of heat adsorption that happens when you go from liquid to gas) and you'll need radiators anyway, like the ones in the back of your freezer. So, you cannot discard radiators.
The gas-liquid transformation do not generate or adsorb heat by itself (well, beyond the losses of the system), it merely
pumps the heat from a place to another.
In freezers you use freon or something similar instead of water, just because the phase transformation occurs at 0ºC (or something like that) instead of occurring at 100ºC, like is the case with water.
For example (this is taken from How Stuff Works), if we were used to live at 200ºC, something like the temperature in your cooking oven, and you climb into your oven (to avoid the freezing 20ºC outside it) and put a flask of water in it, the water would boil at 100ºC, right?
Remember: you're comfortable at 200ºC, so you would feel that the boiling water is cold (because the boling water is way below the temperature you're used to live: it's "only" at 100ºC). So, if you're an alien from Mercury, one of the hottest planets, there you have a way to cool yourself in the hot Mercurian plains: take the water from the atmosphere (water is, of course, a gas in Mercury), compress it, and watch it boil. You could put some Mercurian beers in it to "cool" them at a "chilling" 100ºC...
You could imagine a more efficient way to pump heat than a water pump: what matters is what it's called
latent heat. That's the ability of a material to adsorb heat, roughly put. In the case of a refrigerator, you're using also the
phase change heat to your advantage, as a way to store the "freezing energy", to call it in some way.
There are heat pumps that use lithium or other metals, used in nuclear reactors: they are pumped through electric fields (that is a fascinating part of CFD, called magneto-hydrodinamics).
I believe they are quite efficient (more precisely, they have a high
Coefficient of performance), but heavy, not to mention that lithium and sodium salts are corrosive. This kind of liquid, that behaves like a metal, can be driven or pumped by electricity so, at nuclear plants, the pumps can be serviced: if inmersed into the liquid, the pumps would become radioactive.
Anyway, there you have another way to use the regenerative power: in a lithium heat pump... Moreover, you could use in the design the CFD engineers that have become unemployed after the new regulations.
You could also use what is called solid state heat pumps, that work by magnetizing and demagnetizing gadollinium, pretty exotic and
there are claims that they can cut the power consumption by 40% (yeah, sure).
No! the gas is not cold inside there, it is its decompression that makes "cool". How?