All I can tell you is that if I stay in the house too much, even in the winter, I get very dulled-out and brain-dead. Getting out into the fresh air feels so good, even though its cold, that I go out anyway...even if I just bundle up and sit on the porch. Btw, I saw a robin today, and I'm on the 41st parallel.
A very similar question can be found here:
Here is a link to an article on the benefits of outdoor exercise that may point toward a possible answer http://bit.ly/gMnfuL
Personally I have always found being out in nature to be necessary to my own wellbeing.
Since giving up organized religion, and then becoming an atheist (albeit with strong "spiritual" leanings), I've found experiencing nature to be one of the few things that provides me the same sense of transcendence, and experiencing the numinous.
And there's no denying that those who are spiritually satisfied, through conventional religion or something else, score higher on various intangible and tangible markers of psychological health, and to some extent physical health as well.
I'm of the opinion that it is not necessarily the fact that one is within the confines, such as they are, of a building, but everything else that goes along with it. The implication is that you are more sedentary, that you are less engaged with the world in general and far more likely to have your brain in neutral as you watch TV etc.
Is tramping about outside in the driving rain a more "real" or "natural" experience that is better in some regard than reading a good book in front of the fireplace? I'm not so sure. The desire to quantitatively rank the realism of our experience is itself an abstraction.
I choose to explore the wilds when the desire truly strikes me, not because I feel the need to take a medicinal dose of "nature."
I still believe that the strongest arbiter of mental health is diet and that standard inputs are largely irrelevant, within reason.
I think it depends on a person. I am an introvert, I can spend a lot of time by myself and become more energized and relaxed than extroverts forced to isolation. I feel that would be something similar to what our ancestors were doing in similar weather. Get into a cave, next to the fire, close off the entry and drafts, bury under hides and socialize, remembering great stories of hunting and life.
i don't mind the snow and cold, I actually enjoy it often, as long as it's not extreme. It's tough though in a city when the life stops with too much snow and moving around without a car is a nightmare...