Do I burn more calories in cold weather?

Cold weather wt loss. If you are "cold" and do not wear appropriate clothes for the climate. The answer is a qualified "yes"; a few more but not significant enough to try nudity in the arctic as a weight loss plan. Frostbite could kill you. On the other hand, if you are more active in the winter-ski snowshoe, snowboard, shovel snow and don't compensate with more food, you can lose weight and become more fit.
In theory yes. It is true that metabolism revs up a little to prevent hypothermia (we are "warm blooded") however it is not enough to loose weight and the risks outweigh the benefits so don't try to chill off your weight.