Hi there -
This sounds like what you suspect, probably a chest wall irritation due to muscle strain due to tensing in the cold, or possibly even pleuritic
pain (similar) due to the cold, dry air being inhaled. While generally not at all serious, it can be somewhat debilitating, especially if the
pain on taking a breath is severe. Normally this type of problem will respond well to over-the-counter non-steroidal
anti-inflammatory pain meds such as ibuprofin or naproxyn. If one of these is not effective then you'll need to be seen by a doctor. Usually, though, these types of medications will resolve the
pain and allow the affected muscles or chest wall lining to heal.
Hope this helps. Best of luck to you.