I don't recommend trying a one-day traverse with an overnight pack unless you are in Olympic shape. I'd give that advice in summer. In winter, you go when the conditions will let you, and you bail at the first sign of trouble. Camping by LoTC or Madison hut only saves you a couple of hours of hiking, you're better off sleeping in a motel and starting earlier and traveling lighter. If you plan to carry camping gear, plan to spend two or three days on the traverse.
Even in a year with more normal amounts of snow, the above-treeline portions are pretty windswept. You might well find that you never use your snowshoes (but if you do need them, you *really* need them.) You'll find some bare, icy patches, and some shallow snowfields, and some drifts. Haven't been there lately but I suspect there's been enough snow to fill in the cracks, so it won't really be any rockier than usual. Check for recent conditions reports on trailsnh.com