Lower temps make a big difference when you have an intercooled turbocharger!

 

This may be simplifyig things, but when you are freezing your a$$ off the a/c isn't dragging on the engine. You're also running the heater which means the coolant takes longer to get back to the engine and will be cooler.

 

Correcting the horsepower of an engine for change in air temperature and air pressure has been known since the 1920s.

Standard HP in the USA is measured at 77 degrees F

How much extra HP do you have at 17 degrees F ?

The answer is on page 415 of the Bosch Automotive Handbook,
but other books certainly have it, like Marks Standard Handbook
or this book:
http://www.sae.org/technical/books/R-382

You have to know that the degrees F scale needs 460 added to it to make a 'true' temperature scale,
and you have to use a scientific calculator like the one built into every version of Microsoft Windows under Programs...Accessories..

The way to make the HP correction for both temperature and air pressure
{and how to test whether a CAI improved anything}
has been answered in past posts
like this one:

https://dodgeforum.com/m_935994/tm.htm