The relationship is somewhat spurious, but the old wives' tale *might* have a kernel of truth to it. If the body is cold for an extended period of time, it goes into a conservation mode, to keep the core warm. It does this by constricting capillaries first, to prevent too much heat from being wicked away near the surface of the skin. Then, it starts to slow the cardiovascular system down further, to save energy. It's when the circulation slows and there's less blood being pumped around is when infections can get a foothold in the body. Colds are caused by viruses, and they need certain environments in which to thrive. The lack of normal body functioning, such as lowered circulation, decreased lymphatic activity and less oxygen/toxin exchange (all of which can be brought on by being cold as well as other reasons, such as recovery from another illness, excessive alcohol consumption, etc.) all allow viruses to flourish IF they are present already in the body or enter the body during this time. So, directly, there isn't a connection. But there is an indirect one. Most old wives' tales have SOME truth to them. That's why they've stuck around for so long.