I've hiked from the South Rim two or three times in March. The last time I was there in March, I arrived at the rim during Arizona's largest snowstorm of the year, yet the snow ended about 2,500 feet below the rim. I found that my YakTrax were sufficient and were needed more for going back up, when the trail was icy, than when going down. There definitely was no use for an ice ax.
Another thing to keep in mind: In March, it will be cold on the rim, perhaps below freezing in the morning. But once you get halfway to the river, the air will be much warmer, and you'll have no use for your warmest clothing. You can save weight if you're willing to be chilly for the first couple of hours of hiking down.