I can't attest to whether these roads are plowed and I'm not sure what kind of mileage you're looking for but here's some more info:
Starting at the AT parking area at the intersection of Route 11 & 30 in Manchester area, and hiking North, it's about 1.7 miles to the new Bromley Mountain Shelter and then one mile to the top of Bromley. A longer and _much_ tougher hike would be to go from Route 11/30, over the top of Bromley, Styles & Peru Peaks to the Peru Peak Shelter -- a total of 9.8 miles, one way. Styles Peak also has a nice viewpoint and the shelter is situated in a pretty spot near a river.
If you hiked south from the 11/30 parking area, it's 2.8 miles to the Spruce Peak Shelter, which is the one with the door. I don't remember Spruce Peak having any views, but if you continued on for another 1.1 miles (partly on a dirt road) there is a nice view of the Manchester Valley from Prospect Rock. It wasn't well marked though, so it may be tough to find in the snow.
It's tough to make a good overnight trip in the area because most of the access points are fire or dirt roads, so they may not be plowed in the winter. If the Arlington-West Wardsboro Road is maintained in winter, you could hike Stratton Mountain and stay at the Stratton Pond Shelter, which is another great AT hike in that general area. It's seven miles from the road to that shelter.
All of these ideas, assume you don't mind backtracking on Sunday though.
Hope that helps!
- Ivy