One thing that makes this a difficult thing to answer is that including the parks in Utah, you are looking at a big difference in elevation.
Grand Canyon NP - 7,000' at the south rim
Zion NP - about 4,000' at the Visitor Center in Springdale.
Bryce Canyon NP - 8,000'-9,000' at the rim
Arches NP - 4,000' at the Visitor Center
March is rainy season for Zion. Bryce might still have snow. I'd go late March or early April. You'll still need jackets for Grand Canyon and Bryce but Zion and Arches will be reasonable temperatures.
Are you doing tours of the area? Road Scholar has some very good tours of these areas although definitely not in depth.