It depends on HOW cold it is. Low enough temperatures can cause ice crystals to form in the lungs, which is definitely bad. Same token, in warmer (but still below freezing) temps, your sweat can freeze in your clothes, which can lower your body temperature dangerously (which is why in snow survival situations, you actually get naked before snowshoveling, to keep your clothes from getting wet). Also, your body burns more calories in extreme temperatures (either hot or cold) to try and maintain homeostasis. Many athletes use this trick when they have to make "weight" (by running in garbage bags etc) BUT it's not healthy, and can lead to a calcium magnesium imbalance, and/or shock/stroke because the nurtrients get burned soooo fast. Think of marathon runners who collapse. It's that sort of thing, but caused by the body burning energy to combat the weather rather than the distance burning it away.
Obviously those with lung conditions (asthma, pneumonia, etc.) are far more sensitive to atmospheric conditions than the average person.
So CAN running in the cold be bad for you? Yes. Is it usually? Nope.