If it was that easy, you'd think they would have already invented it...man, I hate how many stories depict the otherworld as stupid. I also think it's funny that water magic can create a "refrigerant" (the big roadblock to commonplace refrigeration) out of nothing.
Refrigerant is not the issue there are many common refrigerants, like ammonia, propane.
The roadblock to refrigeration is the ability to produce, compress and store gasses. The first of what we would call a real air compressor was in 1829, people had been experimenting knowing that the evaporation of liquids could drop temperatures such as evaporating solvents under vacuum since 1804 and some experiments earlier. It wasn't until the invention of the air compressor that the first working compressor based closed loop refrigeration cycle was made in 1834
In addition, idk if the translation was wrong, or the author was wrong, but refrigerant does not become fully liquid during cooling or compression in most cases and he just needs an expansion valve (small hole) to turn the liquid into really cold gas