IF the air supplied is in the form of compressed air, coming from a steel tank that remains more or less at ambient air temperature, the air supplied through the hose will as a result be a few degrees cooler (depending on the pressure of the compresses air and a number of other factors as well)
This would be one way to supply cooler air.
Another way, like suggested above, would be to have air supplied to the unit from a central cooling unit. Now we could do this cheaply, as theoretically we could use a pure water source system. That is, we have water cooled air that is cooled to the temperature of our ground water -c. 55 degrees F. and that would happen to be the exact temperature we want. Water source heat pumps for residential use need to have a secondary heating/cooling unit to bring the air from the 55 degree water temperature to comfortable room temperature, but we could eliminate this step. The disadvantage would be an open-ended lop would generate a lot of waste water, and a closed loop system is expensive and requires a good bit of land to implement.
By the time it passes through all the pumps and pipes and everything, water straight from our well
(no softening) comes out of the faucet at around 60 degrees.
for hobby use for a single individual this may not be worth the effort.
However, for commercial applications, aging and storing cheese is a pain in the neck. It is expensive to maintain the climate in a large room -large enough to house the shelves full of cheese, walkways, and a place to keep all of your stuff for caring for the cheese. If we can only worry about maintaining the climate at the spots where cheese is (which comes out to maybe 1/3 of the volume of the room, if even that) then we have a different scenario.
This is especially attractive when we consider that I would implement this in a cellar which already maintains a mean temperature slightly above the target temperature range (our biggest difficulty is controlling humidity, which is easier and more precise in a smaller space). So heat gain from the outside environment is going to be minimal for me(even more minimal with a positive pressure system).
For me, I can consider some fairly elaborate setups since I would be running enough of these to store 200-300 30-40 # cheeses at any given time, or something like that. This means a number of units controlled from a central source.
For a hobbyist, the most practical system to implement would probably be a unit relying on a thermostat and an electric refrigeration unit.
Then of course, there is the possibility that if you develop the idea and get something that works well, you could sell them.