If you are planning an overnight, the RMC huts on the north end of the Presidentials make a good base for a two day hike. Gray Knob is winterized and heated (to some extent). Crag Camp sits on the King Ravine -- also open in the winter. From there, you can hike Madison, Adams, Jefferson or, if you are fast and get an early start, Washington.
You can leave a car at Lowe's store (safer than parking at trailhead lot) and hike up Lowe's path to reach the camps. They have access to a water supply, so no need to melt snow. There is a charge for staying in the camps ($12). http://www.randolphmountainclub.org/sheltersinfo/grayknob.html
You can sometimes get a good, current description of the trail conditions here: http://www.viewsfromthetop.com/trail/nh/index.html
Have a great trip.