Well you want to consider how much time you will actually be spending outside in the colder climate. If realistically your not spending much time at all then, consider dressing in lighter clothing. Layers would be good something that you can take off easily and possible even put into a bag quickly once your at the airport. remember the airport is heated and the plane will be too. Your only real concern is being comfortable from the car to inside. I would dress light with a warm sweater (once again one that you can quickly put in your luggage once your at the airport). Jeans and a either thin long sleeve or and short sleeve shirt of some kind. When you arrive at your destination, your more than likely to go straight to your hotel, once their you can change into a more suitable outfit for the weather.
The best way to dress when you are traveling and the weather will be changing from cold to hot is to make sure that you are dressed in layers. Also make sure that you know how the weather will be so you can also pack appropriately for the entire leg of your trip. As you get closer to your destination you can begin to remove clothing to accommodate the warmer climate.