This is my problem: I normally leave from a warm place and arrive in cold place. Connecting is a non-issue as another said, you won't leave the airport.
Often it is quite warm when I am traveling from LAX to a cold weather destination in Europe (generally, Paris or Venice). I layer-up from home, carry on a coat so that I'll be warm at my destination (also saves weight in baggage). Having said that, nothing is completely predictable. Once, on a RTW, I brought a fur coat and a rain coat for travel in February. We had great weather in Europe and never had to wear either of the coats. When I arrived in KOA on the last leg of our trip ,it was raining like crazy and unseasonably cold. Had to dig around for the rain coat. You can't predict or prepare for every situation. Make the best of every travel situation.