Is there a connection between being cold and catching a cold?
No, there is not. The incorrect association developed for many reasons.
People close their windows in winter, so air contaminated by virus particles is not diluted by "fresh" air from outside. This makes it easier for the virus to spread. Also, the cold, dry air of winter makes the mucous membranes in the nose swell. This produces the "runny nose" we often associate with an infection caused by a cold virus. Why Don't Penguins' Feet Freeze?, edited by Mick O'Hare