I think they would be more concerned with the “what ifs”. I was always told to wear your coat in the car and not have the heat on as high in case you were ever in a wreck and were exposed to the cold while unconscious or immobilized.
That being said, I would probably court pnuemonia, too.
Pneumonia, colds, and other respiratory diseases are caused by bacteria and viruses, not by going out in the cold. You might be weakening your defenses just a tich by putting extra strain on your body, but I wouldn’t lose any sleep over it.
I would court pneumonia too. Also woo it, and send it flowers, and make it my own. I hate being overly bundled up in a car, unless it’s a convertible and I’m driving from Fargo to Minneapolis in February.
As per Cecil’s above linked article, the main concern of the OP might be cold stress rather than catching a cold.
However, even a cooled down exercised body will unlikely be stressed by the half minute walk to the car. The heat loss is not instantaneous. Only if there were really strong winds and freezing (i.e., super cooled) rain and a pack of wolves should one worry.
Although, one might want to take into account how long it takes the car to warm up, and, as mentioned above, whether there is warmer clothes in the car in case of a breakdown. At some point cold stress, then frostbite, then hypothermia, then death will set in, at that point, you’re a sitting duck for the wolves.