I've snowshoed/hiked parts of the TRT in winter a couple of times. Some sections were signed with occasional blazes or small TRT emblem signs on the trees and were relatively easy to follow through the snow and trees. Other sections, not so much.
Whem we last hiked part of it (April 2013), the snow was low enough around the Kingsbury Grade to Spooner Summit section that we were able to run quite a bit of it with only occasional snowy patches in the shaded areas. Required a little postholing here and there, and there was a couple of spots where some microspikes would've helped, but otherwise it wasn't bad at all.
On some of the higher sections, I'd expect it to be more of a typical snow travel affair.