We live not far from the Grand Canyon, just outside of Flagstaff. You'll LOVE it no matter how you choose to see the Canyon! Winter is not over here yet in March; the weather can be sunny and beautiful or snowy, just depends... (We're at around 7000 ft elevation; MUCH different climate than the desert Arizona most people think of.)
The Grand Canyon Railway from Williams is really fun but doesn't give you much time to spend at the Canyon if you just go up for the day, so you might want to consider either staying overnight in Tusyan if you take the train up, or staying in either Flagstaff or Williams and driving up to see the Canyon. Feel free to PM me if you need some local info! BTW, there's a WONDERFUL LQS in Flagstaff!!!