In March, the road will be closed, so you have to park at the gate, and walk up an additional 3 miles to the trail head. At some point going up, and likely lower, maybe even at the trail head, you will be walking on snow.
The guiding services that take people up in March and April all use the Mountaineers Route access, going up the North Fork Lone Pine Creek. Usually there is enough snow then that they are able to walk up the valley above the brush and stream.
Whitney in early spring is not a simple walk up the trail.