Of course colder denser intake air *does* give more power, this has been fully established experimentally. The additional air shouldn't cause the engine management to pull timing. More air = more is squished, but it's *colder* to begin with, in colder temps the compressed charge should still be colder vs. in warmer ambient temps. Should be less likely to have timing pulled, I would think.
SAE J1349 Revised AUG2004 (Tc = ambient temperature in Celsius, Pd = ambient pressure in millibars)
http://wahiduddin.net/calc/cf.htm
Running the numbers, this shows a 10C/18F change in temperature => 2% change in power.
To my mind, the only question is how effective aftermarket CAIs are vs. OEM. My guess is: little to no improvement.