Also, this statement is wrong for the current era F1 engines:
The statement is correct for "traditional"turbo engines, as the cooler intake air is more dense, thus it will have a greater mass of oxygen and more fuel can be burned. That's why the extra power.
In the current era engines the mass air flow is no problem, but the fuel flow rate is limited. Cooling the air beyond that required to avoid detonation will not give extra power as no extra fuel can be used, and will have the effect of requirin a larger intercooler system which will negatively impact the aerodynamics (however slightly).