I have had the same issue and found a solution that worked for me. I live in Chicago where we recently had the horrible cold snap. I was still running, keeping up with my winter routine, and what I do is wear a gator or face mask for skiing. As i breathed through it while I was running, it helped to moisturize the air as I breathed, keeping my lungs and throat warmer which was a big help. I haven't had this issue since, so this may be a viable solution if you are not doing something like this already.
As for harmful, it certainly wouldn't seem so. I know plenty of people who have had the same experience and have had no respiratory issues whatsoever.