Moab has been my annual vacation destination for the past five years (minus one year when we went to Escalante, Ut instead). Generally my wife and I go in May, I've never been there in March or April however two years ago in early May we got a lot of rain and some snow flurries at the higher elevations. This past year we we're there in mid-May and enjoyed cool nights and warm days with no rain. A bonus to going later in the year is that the days will be a little longer.
if you have any other questions just let me know. It's an amazing place and no matter when you go you won't be disappointed!