10" of snow in NC? Stay home.

(I was living in SC once when they got maybe half of that. It shut everything down for days.... This was the one: http://en.wikipedia.org/wiki/1993_Storm_of_the_Century)

But to answer seriously, I have a bike with good snow tires and I don't ride in those conditions. As others mentioned, you have to consider that all kinds of motor vehicles will be out of control. I also find that it's not fun to ride in snow that deep.