bear in mind it could be freezing ! We went one Christmas-New Year pre kids and it was very, very cold, little sun and short days. Christmas Day skiing was magical , pistes were so quiet and still, but New Year was manic and very busy. Also bear in mind that the better resorts are several hours drive form Boston so you'd probably need to overnight there rather than fly in and drive straight there. Tuition, especially for kids , is supposed to be great but we're saving the trip for when the kids are older.
We stayed first in Jackson NH (nr North Conway and its outlets !), which gave us relatively easy access by car to several mountain areas,none of which I'd say was a resort in itself though, then Lincoln NH near Loon Mountain and also driveable to Waterville Valley, a resort which has a good family friendly reputation.
hth