I think Moosilauke is a reasonable first winter hike if you really haven't done much in the Whites before. It is relatively easy going up Gorge Brook with a well defined trail, and if bad weather comes it is fairly sheltered in the trees most of the way, and a quick run down to the treeline from the summit. It is not mountaineering.

If you want a mountaineering hike in the Whites, things like Flume Slide, North slide in the Tripyramids, the Chimney in the Osceolas, or some crazy shit on Mt Washington would be my go tos. But I wouldn't do that without some guided practice.

That said, Lafayette kicks ass and if the weather is good it is hard to beat.

Bring usual winter gear like gloves, microspikes, goggles, hand warmers, and an extra extra shirt. Dry clothing can make all the difference.