I read that being in a cold environment weakens the immune response in your nostrils when breathing in that cold air enough to cool off the inside of your nose, where then the pathogen fails to be destroyed as it would have normally had it not been cold.
I recently saw an article on HN (don't have a link, sorry) that said that cold did not, in fact, do anything to make us sick or help us catch stuff[1], EXCEPT that it made it more likely to spread something due to running nose or other contact with body fluids.
[1] it may have been specifically about cold and flu, I don't remember exactly. It was within the past month or two in case you feel like searching...
Air circulation is compromised in the winter because we close all the windows and doors, and generally we congregate closer together.
For a long time that was considered to be the only reason colds happen more in cold weather. This thing with influenza viability would change that (of course, what one study finds another refutes, so who really knows).
Here in Florida no circulation season is April - November. And yet flu season is still winter, the only part of the year where people even consider opening windows.