It's going to depend *entirely* on whether the trail is broken out. The AT/LT in that area could be quite difficult to even *find* if the snows are deep and it hasn't been traveled.
Assuming you are able to follow it reliably, if you have to break more than a foot or so of fresh, that day from Melville/Nauheim to Goddard could be a long one. It's certainly doable, but it'll be plenty.
The trip out, of course, will go faster -- but most of that descent is not nearly steep enough for butt-sliding or sledding, so it will still be a long trudge.
Edited to add -- if it were me, I think I'd want to do some kind of a shakedown winter backpack, closer to the car, before heading this deep in. That's a *really* remote area. If something runs off the rails, help is a long way off.