It all depends on a few things:
#1 If Arizona law requires it, then yes you do.
#2 If you don't mind the sound, then no unless #1 is yes.
#3 If your wheelin' pals don't mind the sound, then no unless #1 or #2 is yes.
If you are concerned about legality then you should contact whoever is in charge of offroad areas in Arizona. In Oregon we have laws about noise and spark arresters for different vehicles, and I would think all states do.
So how loud is it w/ no muffler? Does the exhaust run all the way out the back still?