Cold air tends to be very dry, which can most definitely irritate your nose and throat (among other body parts). That irritation and drying out can make the thin skin and mucous membranes more vulnerable to attack from bacteria and viruses.
The only really unscientific part of your post is that the cold air itself is not the direct cause of illness.
People with a strong immune system might not see a big difference, but if you are already more susceptible to getting sick, then the link to cold air may be more obvious to you.
Cold air tends to be very dry, which can most definitely irritate your nose and throat (among other body parts). That irritation and drying out can make the thin skin and mucous membranes more vulnerable to attack from bacteria and viruses.
The only really unscientific part of your post is that the cold air itself is not the direct cause of illness.
People with a strong immune system might not see a big difference, but if you are already more susceptible to getting sick, then the link to cold air may be more obvious to you.