Kaysie, like you, I don't need any cooling systems because I have a nice basement. But, I thought I should point some things out just in case someone wanted to try this.
Air is terrible working fluid because it's specific heat is so very low. To illustrate this, I did a quick back of the envelope calculation:
Assume: 10 gal of water to cool from 80F to 70F
Tank is PERFECTLY insulated from surroundings (no heat gain)
Air lines are PERFECTLY insulated on the run from fridge to tank (no temperature rise)
Air is supplied at 30F at a rate of 0.35 CFM (per Air Pump AP2 model at maximum operation - note: could be better pumps out there!!)
Total energy to reject to achieve 10F drop - 355kJ
Using thermophysical properties of air at 350K gives a required volume of 30F air of 9m^3 to cool the water. The referenced air pump would require 15 hours to supply that much air!! I can supply all details of the calculation if you'd like to see it.
Now, in reality, the tank is transferring energy with the surroundings during the process and thus the actual time will be MUCH longer! I didn't research air pumps very much so there may be better performing ones out there but I don't think you're going to find one in a decent price range that can move the volume of air needed to cool water in a reasonable time frame.
Now, you may point out that I'm talking about the transient cooling event where you state if you can get it that cool, the air will maintain it. The cooling rate on the air system detailed above works out to be right at 5W. We would have to make some wild guesses about someone's environment to tell if the system could actually hold it at the required temperature but my gut feeling is that most people who are looking into cooling systems will have a higher environmental load than 5W.
My advise as a thermal engineer is to not bother messing with forced chilled air for cooling water. Air is useful for cooling in the following situations only:
a)evaporative cooling
b)cooling things that are VERY hot
c)cooling things that are VERY small
d)when you can move massive amounts of air (like the system in our homes)
If I'm going to rig up a cooling system based around a mini-fridge, I'm going to use a closed water loop.