Just as a comparison, I rode in this morning for 12 miles on untreated/unplowed MUPs with 1-2 inches of fresh and packed snow and icy ruts. I did lower the tire pressure to 40 psi for better snow traction. No slipping whatsoever with the Marathon Winters.
I don't think I would ride in a blizzard on any tires, but would certainly want studded knobbies like the W240 in more than a couple inches of snow.