IMO to do the tic and not epic:
Go North to South. Hike up to one of the cabins on the slope of Mt. Adams and hunker down, waiting for your day. Many winters have a succession of little storms with relatively calm periods in between. This is a serious mountaineering undertaking, so get an alpine start, long before dawn. Knock off Mt. Madison when you first get up there or while you're waiting for your day so you don't need to turn left to pick it up on the actual traverse-- unless your personal style requires doing it with all the other peaks. (I work in business so I have no sense of ethics whatsoever.
While the days are longer in March, you are statistically much more likely to have gale-force winds that month than in February; you can look it up.
Be extremely fit (i.e., in good shape for carrying a pack uphill for a long ways for a long time). Go with somebody who is equally fit because if you get hypothermia, you may well not realize how irrationally you're acting, plus a companion can tell you your face has frosted. Do not get more than 100' apart on the traverse because you'll get chilled waiting for the slow one, and the slow one won't get good rests. But don't plan on taking sit-down rests.
Carry a sturdy little shovel so that if you are not able to make it all the way in a day or if a storm catches you, you can dig in. Do not try to sit out a storm in the open!
Don't start the traverse in a whiteout; you'll be too slow picking your way along. Pre-research the escape routes; most winters you don't want to go over the lip into any of the ravines; it's better to take the ridges in between, like Lion's Head (which has reflectors on the trees for night descents). Raymond Cataract sucks, but you probably won't die. Etc.
Depending on conditions and fitness, you should be able to get from Adams and over Washington and down from Lake of the Clouds in a day; most parties don't seem to do the Southern Presidentials in the traverse.
Best of luck and weather!