From my experience, snow flies around from left and from right and from top, and when snow hit yr camera or lens, it will melts gradually, and becomes water droplets, so before the snow melts u should wipe it away as much as u can. The best is still using a rain jacket, cheap one will do, or get a cheapo plastic bag to cover. It will also help to reduce a bit the condensation and fogging effect when u walk from outdoor (cold) to indoor (hot).
When the snow fall on your lens, it becomes water just like rain. It is a bit irritating when you are trying to take pictures because you have to keep wiping your lens or either find a shelter from the snow.