Class C's generally behave reasonably well in winter conditions, all things considered; they have decent ground clearance (though bad departure angles, but that's a different story) and plenty of weight over the drive wheels. The couple times I've had mine out in moderate snow conditions it's been just fine. I have no desire to push things; I imagine that if it started to get out of hand you could cause all sorts of damage and mayhem pretty quickly, and so do not care to explore the edges and limits of handling in snow or otherwise.
As always, good tires make a big difference, and there are limits on what you can do, and for goodness sakes please be careful, and so forth.
(Also take care if they salt the roads to thoroughly clean the undercarriage and underside of the motorhome as soon as practical; the framework many RV makers add is none too thick and none too well protected from corrosion.)