I've snowshoed to Trail Camp a bunch and it all depends on which winter you are talking about. We had a MMWT to the summit trip planned in January but canceled the summit as the destination after it snowed for the first time that winter a few day before the trip.
I have never planned an attempt on the summit in the dead of winter with snow about.
I will say, the most fun I've had in this area is in the winter and the furthest have gotten is Trail Camp. The MMWT in winter is a heck of a good time...more fun than summitting in prime time.