HS ball in AZ starts the last weekend of February. Almost every weekend in March has an invitational HS tournament scheduled. If you are looking for warm(er) weather, look in the Phoenix, Tucson, Yuma area. Most of the Az Interscholastic Association sanctioned tournaments are listed here: AIAONLINE.ORG :: USE OF AIA FACILITIES CALENDAR
There will probably be many more added as the spring draws closer. The Tournament on Champions in Bullhead City March 13 - 15 is usually pretty good. 35 - 40 teams from several states across the Western part of the Country. They have hosted teams from Texas, Tennessee, and Florida in the past. Usually very good competition with some very good teams.