There has been so much debate on this.... All the "serious" articles I've read (written by engineers, not by marketing dept.) mention modests gains but nothing like some companies that sell CAI want us to believe. Colder air is more dense, so more power but only to a certain point cuz we are also limited by the compressor inlet (fot N/A engines, an intake -especially dynamic- can make more of a diff.)
Anyways, it all depends on how testing is done which boils down to scientific "honesty". For instance, I was surprized by the dyno sheets that a very reputable company (BMC) is showing with their dynamic carbon intake, they seemed low (about 4-6 HP) compared to the likes on Injen AEM..., but I trust their testing waaaay more (they made filters for the Ferrari F1 winning team). So I figure that about 4-5-6 WHP is what we really get with a CAI, more than that is prolly just a marketing hype IMO