Mid-April through the end of May is generally the best time for good snow conditions on the MR. March is definitely mid-winter up there, not late-winter, and snowshoes to get to Iceberg Lake are likely still required. But it depends on the recent storms, your phasing relative to them, whether you are following others' tracks, time of day, etc. Mid to late March could be OK, but I wouldn't count on it. The last few years, though, have been pretty good.
I checked my log for March ascents of Whitney and other peaks accessed by the Portal road, and found 6 where I had made notes where we parked: 1985 (got to 7200'), 1992 (Meysan lot), 1999 twice (Portal both times), 2002 twice (Portal both times). But this is skewed because if winter storms dictate parking down at the Road Closed sign, there is less of a tendency to go for a climb here - hence no entry in my book.
Bill is right. It depends much more on the recent weather situation than the month, in winter.
If you have climbed the MR in summer, the route finding will be trivial for you. If you haven't, but can read a map and altimeter, and have done your homework, it is almost trivial. By March, there is almost always enough snow below LBS Lake that you will be going up the couloir instead of negotiating the Ebersbacher Ledges.
People worry about the last 300' above the notch at ~14000'. In winter this is just steep snow. You'll use ice ax and crampons, of course, and many people like to belay on it. Especially coming down.
