There can be a number of factors. Besides the increased exposure that you mentioned, getting chilled is stressful to the body, weakening the immune system. Probably not all that often that happens nowadays though. I think a bigger factor is that we can't get vitamin D from sunlight in the winter, and the vitamin D reserves that we've stored in our fat deposits get depleted as the winter progresses.
I was getting 15 minutes a day sun at its apex, but now the sun has dropped below 50 degrees at its max midday height where I'm at [good vitamin D UV rays bounce off the atmosphere at less than 50 degrees incidence].