Conditions right now seem to be bombproof crust rather than waist-deep snow. Crampons are probably much more important than snowshoes, though both should be handy.
What other peaks have you climbed up here? Do you have experience in the winter above treeline? If the answer to the last question is no, I'd suggest something smaller (but still wonderful) to start. A trip like Moosilauke from Glencliff, Jackson or Pierce from Crawford Notch, or Mt Liberty from Franconia Notch might be a good choice.
If you have some serious winter mountaineering experience than a trip up Madison or Adams would be a good choice. Keep in mind that temps this weekend will be bitter cold, single digits at best. The Mt Wash forecast for Sunday is a high of 3F with high winds. Not a great day to be up high.
-dave-