Hike into the Havard Cabin and spend the night!

What good does that do you on the traverse? the walk from Pinkham to Harvard Cabin takes like an hour and involves fairly minimal elevation change.

I stayed at the Harvard Cabin two new year's ago to do the winter lion's head.

how about a reservation at the observatory?

If you get the weather on your side and snow conditions are right the traverese can and is done in a day.Can't count on the conditions to be right.Me and a partner once climbe Washington up and down in 3 hrs 45 minutes.The snow was perfect,everything was whited out above Lions head,but we made time coming down .Glissaded agood part of the cone,all the lions head,then for some reason ran down the cattle trail[ I think to get away from the goofers].I've also spent 8 hrs to go from a camp partway up Madison,to the summit and back to camp.Low snow and wind up to 110mph made things slow going. Bivy gear,if you carry it you will use it,if you don't you might need it.

mmm... wasn't specific enough. If the traverse is too much, a stay at the Harvard Cabin is fun, and then do a summit push, hike the Lion's head's trail, etc etc etc.

it builds character. Mountaineering,the art of suffering.

stayed there once.I thought I was in Boston. Rather slep out in the snow.Thins out the crowd.

I had a nice night at harvard cabin (no not that kind). I would go back.
I would also consider sleeping down in the valley and tagging some peaks from a base camp. Above the tree line in Nh and the dacks is (multi day) serious stuff and may be more than you would want to handle if this is your first winter trip. And I would not go alone or with someone who is even less experienced.
If the weather gets bad while you are above the tree line you could be in serious trouble, thus my suggestion that you camp in the valley (or someplace below tree line) and hit some peaks, weather providing. Be careful, people die every year during winter in NH.

The Whites are nice. The Traverse, depending on your skills might not be a good idea. There is tons of hiking/peak baggin to do up there. Weather will dictate what you do but even if it is crap, there are still tons of things to do.

Climer

attached pic from my last Whites trip.