We all secretly know that you can catch a cold from exposure to cold, but science says "no."
"Exposure to cold weather will not give you a cold because colds are caused by viruses, says Professor Raina MacIntyre, adding that there are around 200 viruses responsible for the common cold." — Professor Raina MacIntyre at ABC Factbuster.
This is like saying I ate a sandwich because I had a sandwich in my hand, when really there are many factors that lead me to eat a sandwich.
Now, science has a new idea: having a cold nose increases our susceptibility to viruses already present in our nose. We know we live in a sea of viruses and bacteria, and our bodies fight a battle constantly. Exposure to cold may tip the scales so that disease may catch a foothold. OK I don't have a link for this, but here's a link about influenza being more resistant to attack in colde temperatures.
Personally, I know that one time I caught bronchitis from inhaling paint dust. The doors were being sanded in preparation for painting at my office, meaning they were open all day while the sanding occurred. Later in the day I felt a pain in the back of my nose, that became a cold, that moved to my lungs, and that resulted in several days off work. So everybody can stop investigating now, because I've proved it.