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I went last Sept and it was perfect. I would think March might be a bit chilly at times. Probably have to start late morning and end early evening. As others have said, the elevation is a factor. Moab is at about 4000 feet. Heck, I was in Mexican Hat/Monument Valley (same elevation - not too far south of Moab - you should check it out) just two weeks ago and it was 55 degrees in the morning. Yeah, it warmed up to 100 degrees by 2 pm though!
You could easily pick up a nice ride from Moab, to Monument Valley, and then the south rim of the Grand Canyon, and back. That would be a great few days.
Btw - the drive through the Rockies could be very snowy at that time with closings. I would avoid any weekend travel if you are approaching Moab from the east on I-70 due to skier traffic.
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