Yes, Its cold your body needs to produce heat, bulking up on carbs, and fats will help your body produce body heat and energy and you fell better in miserable weather.
The choice of white meat is excellent. White meat do contain less fat yet it provides enough protein.
Do you have anemia? If you always feel hungry during cold weathers, perhaps opt for red meat. Red meat do contain more fat but if you grill the meat rather than fry, then that's ok. Red meat improves blood circulation and will keep you warm.