The trail's terrain is very well-suited to skinning up and then skiing down w/ AT gear or a turn-oriented tele setup. (Which come to think of it is not very surprisingly since it was designed by skiers for skiers by the CCC many moons ago...)
Unfortunately though, snowshoers typically create a trench down the middle of the trail, leaving somewhat narrow skiable banks on each side.
Then again, this isn't a typical snow year, so the more important factor will be coverage as "oisin" notes.
The USFS avalanche report provides helpful conditions info on the Sherburne ski trail, which can be used as a proxy for nearby below-treeline skiing conditions. But keep in mind the lower elevation of the Doublehead trail (from 1472 to 3039 according to my topo software, as opposed to about 2000 to 3800 for the Sherburne). Another good idea is to call the trails info desk at the Pinkham AMC, or the local xc centers (Jackson or Great Glen) since some of their staff ski bc also.