Not the GP, but: While I discovered in the last years that I absolutely need to work out regularly or risk getting depressed, it is especially hard in the winter months. It seems that my body is preparing for hibernation and all I want to do is sleep and eat (preferably with lots of carbs and fat).
I think I will talk to my doctor about trying some Vitamin D supplementation in the next months. Generally I try to avoid supplements, but in this case I don't know what else to try.
It is very easy to fall to low levels of Vitamin D even with supplementation (you need an abnormally high dose at times to get to 'normal'). So, please do check with your doctor. If you do have a deficiency and get supplements, it makes a lot of difference.
In winter you probably also get less sunlight. I'm under the impression that most people would benefit from bright daylight during the day -- I have some LEDs in the daylight/6000K spectrum on a timer at my workstation -- even if you aren't diagnosed with SAD.
Remember to keep them on during the _daytime_ only, though, to keep your body clock on the appropriate schedule!
This is not necessarily the same issue as you're talking about, but I feel like in the winter, doing your workouts outdoors in the daytime can be a good thing.
Some people (including me) find that they stay indoors most of the time in the winter. Doing your workout outside gets you out there, which gives you not only sunlight (speaking of Vitamin D) but also a change of scenery that can cut down on cabin fever.
With the proper gear, the cold is tolerable (except maybe in extreme climates). And, especially if the exercise is vigorous, it's more tolerable being outdoors in the cold than it would be if you just went stood or sat around outside.
I think I will talk to my doctor about trying some Vitamin D supplementation in the next months. Generally I try to avoid supplements, but in this case I don't know what else to try.