I don't find fresh snow to be much of a problem. This is my third winter commuting. What is a problem is that fresh snow hides the ice. I travel a combination of hard-packed bike trail, city streets, and parking lots. After the forth or fifth fall in the last two winters, I broke down and bought studded tires. They have more rolling resistence than regular tires, but they do help a lot on the surprise ice patches that I encounter. Before I started commuting, I would run a moderate knobby traction tire for enjoyment rides in the snow. Nothing prettier than big snowflakes falling and cruising through town looking at store windows during the Christmas season. One of the perks of living in a small town.
Walt