You don't want to run it through turbine blades but even snow or chunked ice that is introduced to the intake path in appropriate amounts will not only benefit from the thermal capacity but for sure be atomised by the time it gets to the combustion chamber.
Think inner inner cooler.
If one can make room for all the associated do-dads with a turbo and an intake cooler, what is wrong with the NA pilots.
Are they missing some power ?
A very famous liner had the best NA engines available that tested excellent on the Dyno.
They failed to produce enough power in the car because the conditions inside caused the inlet temperature to go over 300 deg.
It is not just altitude that sucks your power (money) on the salt, but (heat build up) time and space too.
Just like tires, few realize how hot they really get under load.