Why the exotic working fluid?
Heat is a better choice than cold.
When you compress air, you heat it. That heat is lost, typically, and is the huge reason for the 75% losses.
Build a huge underground water cistern and simply heat the water.
Water has the highest specific heat of any ordinary substance, and that heat can be recovered quite efficiently with a Stirling-cycle engine.
No need to get the water to boil, in fact, you'd avoid that.
Compressed air as a storage medium has a long history. Usually it is found that you need to ADD energy to the compressed air as it expands to get it warm enough to use, a simple heat exchange with the environment is usually insufficient. And in the case of liquid air storage you have the phase-change energy to add back in before you get any gas evolved at all.