The rules for open carry were quite simple in Arizona, when the laws meant what they said (described below) until the late 1990s. Then, several activist judges literally rewrote our laws from the bench, creating "law" that was never passed by the legislature and creating significant risks for the average armed resident.
The new "test" for whether open carry is legal -- not written in any law -- now seems to be, if your gun is readily accessible for immediate use, the means of conveyance must reasonably place others on notice you're armed. The phrases "readily accessible for immediate use," "conveyance" and "reasonably place others on notice" are undefined inventions of the court; "conveyance" seems to imply holster, gun case or other device for carrying a firearm.
The enacted statute applies to adults who are not prohibited from firearm possession. You may carry firearms, loaded or unloaded, throughout Arizona, subject to the following restrictions. If you carry a gun on yourself and don't have a concealed-weapon permit, the statute says it must be at least partially visible or in a belt holster that's at least partially visible. See §13-3102 for the letter of the law. The statute says you may also carry a gun in a case designed for carrying weapons or a scabbard, and the case or scabbard must be at least partially visible, or else carried in luggage.
The simple, long-standing partially visible standard has now been reinterpreted by some courts to practically require blatant display, and they have invented other non-statutory conditions that place honest people bearing arms in jeopardy. Specifically, some judges may seek to increase your risk -- not written in the law -- if you're on foot and your gun is readily accessible for immediate use (which a gun in a holster obviously is). Under statute, "immediately accessible" conditions only apply to vehicles, described below.
In addition, the law does not define what a holster or weapon case is or looks like (common sense used to apply), but in 1995 an appellate court set a precedent by saying a fanny-pack holster does not qualify -- it doesn't look enough like a weapon case -- without saying how much is enough. This created enormous risk for decent residents everywhere, and the court didn't seem to mind. If you're carrying openly but someone can't immediately tell, you may be held in violation. Yes, that's right, it's confusing.
Authorities and lower courts have been inconsistent in dealing with people who carry openly -- from completely ignoring a person to court convictions -- creating a substantial degree of risk, and who wants to be the next test case. The risk is pretty much eliminated, however, if you have a concealed-weapon permit, or if you carry openly in a manner so that people can't mistake that you're armed.
There is a certain pride that Arizona is an open carry state -- it reflects our pioneer sense of freedom. Indeed, many states have made it much harder to move a gun from point A to point B than it is here, where people are (or certainly used to be) free to take their firearms around pretty much as they see fit.