It will be winter weather, but most of the parks and monuments will not be closed. Flagstaff area, Grand Canyon, can get a lot of snow by March. Access to South Rim is kept open, but not necessarily the whole South Rim Drive.
With December-March travel times, and where you have to go to get to the lower, drier, warmer parts of southern Arizona, I assume your RV is fully winter capable, which is all that is needed to use it in northern Arizona and Utah during winter.
Tom Test
Itasca Spirit 29B