Refrigerants have to be compressible to increase their temperature above ambient. Or equivalently, to be expandable to cool them. Salt water wouldn't work at all.
It's not a very good one for general space cooling for the reasons others have stated here, at least near typical ambient conditions. Water / steam are often used for space heating, though there the energy conveyed is typically from combustion rather than via a heat pump as in an air conditioner.
Water does work well for cooling high-temperature equipment such as automobile engines and power plants.
Both typically operate at or above the standard atmospheric boiling point of water.
Water is a very good heat transfer fluid, it has a huge specific heat capacity compared to many other fluids, it's cheap, abundant, non-toxic, non-flammable.
The problem is that if you want to reduce the temperature below ambient you need some kind of expansion cycle, either with a single-phase gas, or something that has the gas-liquid phase transition somewhere in the temperature of interest. Water doesn't really work for common AC or refrigeration uses.
Water could be used at lower temperatures in a low-pressure system, which would reduce the boiling point.
I'm curious whether or not such a cooling design exists, and what application(s) it might have.
For HVAC, I suspect the temperature would have to be between 0 and 8 C (32--45F), which would be about 5--10 mbar of vacuum.
Note too that it's difficult to cool below 0C (32F) with water, though salt water can reach lower temperatures. Other refrigerants function far better down to ~ -8 -- -12C, or lower. Water-based refrigerants would likely require a secondary cascade.
The problem is that if you lower the pressure enough to move the boiling point to something suitable for AC or refrigeration, the density of the steam will be very low. So you'd need huge pipes to transfer that heat around.
