My friends and I did some riding on the TMT, where it starts down south. It was totally fine from the Mass border to Becket Road, just north of 23. There was impassible snow on Becket Road.
It seemed like if you were above 1500' in elevation there was snow covering the roads. (We rode other stuff in the area.) Below 1500' and most of the snow was gone and the mud was not an issue.
Give it another 2-3 weeks if you want to ride the whole thing.