Other than the steep section going up C-Dome (which is not the entire trip up from the notch but maybe 1/2 a mile or so & you will also be doing it when you are freshest - given a choice of up or down, I'd send you up it) it's a good trip.
Up to the hut is pretty easy, as you approach the actual notch, it gets a little steeper & it's a moderate descent to the lake but not bad. (better with lots of snow) Since the hut is open all year, it's usually well broken out unless you are 1st on it after a foot (or more) of new snow.
Of the open winter huts, it's probably better than Lonesome & either the Kinsmans or Cannon. Getting to that hut is easy enough but getting up Cannon from the notch has a real steep section & in the current low snow conditions, getting up to Kinsman notch may be tricky in a few spots. (check conditions, with winter peakbagging, there will be reports & trail conitions posted regularly)
Zealand Hut requires a trip up the closed road Hale would be easier & the trip up to Zealand Mt. (a viewless trek except for the great view on Zeacliff & a couple of other spots).
From Crawford Notch, some good choices, Willard or Tom or Pierce probably the easier ones as the top of Jackson can be tricky & getting up Field is steep (not like others but a decent slog) in places before & after Avalaon.