Snow doesn't make you damp unless the temperature is close to thawing, as the clothing insulates the snow from the body warmth. You can just brush snow off you clothes when it's cold enough (a few degrees below zero) until you get indoors, of course. Getting wet from the inside due to sweating is a much greater threat (which I guess Privateer's first link explains).
When the fur is wet, it insulates much less (there's another topic by me that shows picture from research done on this topic. Even polar bear fur has a huge decrease in insulation capacity when wet).
So there must some cycle: the snow melts very slowly on your clothes (because insulation is never perfect), but this wetness in turn makes the fur less insulating, thus speeding the snow-melting. I have no clue if the melted snow would freeze again faster than the body temperature can melt it, though.
Anyway, one could just exclude snow from this to make it still interesting, I believe, for all the times the temperature is above freezing and for when one enters the water.
I still think that, purely on gameplay terms, having to protect yourself from snow during the coldest weeks of winter (especially when coupled with wind) is extremely compelling. Much more interesting than any sweating penalty that requires you to fine tune your clothing, which is very tedious in such a game (as Sami also says in the first topic linked by Privateer).
Plus weatherlore would actually make sense.. skiis wouldn't be enough to travel in winter, you'd have to know if there's a storm coming.