Southern AZ weather is such a crap shoot during March: it could be freezing; it could equally be sweltering. The sun will already be getting hot by then. And temperatures can change drastically within 24 hours.
Once you get into April, you will be looking at hotter and hotter days with cool/cold nights.
As for snow — who knows? It changes year to year, so predictions will only be possible a week or so before your trip.
I'd plan on taking a relatively warm sleeping bag/quilt, similar to what you'd bring for the PCT after the desert portion (something like a 20F).