Under most circumstances, cold weather shouldn’t be a reason not to run outside. The main concern with winter running is the lack of daylight, the footing, and the snow banks narrowing the roads, and not the cold air.
Often runners assume cold air will damage the lungs, but the cold air is warmed by the respiratory passageways before it reaches the lungs. The discomfort felt breathing in cold air is due to the lack of moisture in the air. Cold air is very dry, and it causes runners to experience a dry sore throat and/or dry cough after running. Over time the body will adapt to the environment and less discomfort will be experienced. Using a scarf or bandanna to cover the nose and mouth will help pre-humidify the dry air.
The nose and mouth will frost bite long before the lungs will freeze, so runners should use extreme caution and respect the cold. The key is to have the proper running clothes to maintain body heat, insulate the body from the cold, and protect the skin from the wind chill. Dress in layers and use a base layer made of a technical material like CoolMax or Drylyte, which keeps the perspiration away from the skin.
The running gear and experience of each runner will determine where to draw the line of what temperature is too cold to run in. I draw the line for myself at a wind chill index below -20 F for runs that will take less than 40 minutes to complete. For longer runs, I draw the line above a wind chill index of 10 F depending on the distance. It is possible to run when it is colder, but I don’t think it is worth the risk.