The basic idea of cooling the inlet air to an engine or turbo is a somewhat reasonable concept but in the real world ..... very limited applications. In the racing worls....not a chance.
If the turbo has a pressure ration of 4 to 1, net outlet pressure of 45 psig (300 kPa) an intake temperature of 20 deg C, the outlet temp. will be upwards of 180 deg C even with outstanding efficiency. In order to put the cooling at the front end (ahead of the turbo) you should be able to guess at the temperature drop you would need to achieve the same effect.
Big advantage of the after turbo or inter-cooler is that the temp. difference across the cooler is HUGH. At a delta of 160 C deg. the cooler will be an order of magnitude smaller than if the difference were only 40 C deg. Try packaging the latter into a side-pod.
Is there still a case for pre-cooling the inlet??...well yes there is. Beyond ensuring the inlet air to the engine or turbo is as close to ambient as possible, there really isn't a place for inlet cooling in circuit racing.
One place where it does have a real application is in gas turbine power plants. Those subjected to high inlet air temperatures.http://www.tas.com/
By judicious use of large chilling plants to cool the inlet air, the output derating at high ambient temperatures can be avoided and the net power available for sale is increased. Even after considering the power needed to run the chilling plant, it can still pay off in avoided additional units or better utilized smaller units.
Personal motto... "Were it not for the bad.... I would have no luck at all."