Medical Student here: I could be wrong but, essentially from my understanding, immune systems are basically inhibited by cold air making contact with the lining of the respiratory tract, reducing the ability for immune response within "cold area". So the respiratory tract then becomes more vulnerable to infection (viral or bacterial types). This too can happen when the body as a whole is exposed to cold for long durations of time, as the body prioritizes remaining warm over protection from pathogens. There's obviously TONS of more detail to this.