CAI's also typically allow greater airflow due to their less restrictive filters. The more air flow the more fuel you can add and the bigger the bang! And we know bang=horsepower. Like woodj said the more dense cold air means more air per unit volume in the cylinder than the warm and less dense air.
It all about air quantity!! That's the whole concept behind a supercharger. You compress the air so you have more air mass per unit volume in the cylinder + more fuel (A/F ratio stays constant) = even bigger bang so even more HP!!! Muhahahahaha!!
