By statute, a gun must be in a holster, map pocket, center console, glove box, or plainly visible (on the seat, etc). The statute makes no difference between holstered on person, or holstered elsewhere.
Unfortunately, the case AZ vs. Adams muddied the water a few years ago, and the court decided that a holstered weapon on a person, which otherwise would be 'open carry', is concealed in the context of being seated in a vehicle (basically concealed by the vehicle).
It is bad case law, and the legislature has been trying to address it to make the law as written specifically void Adams. Unfortunately, our budget fiasco precluded a lot of good legistation this last session.
In the current environment, to be 100% safe and legal, the firearm must be plainly visible (on the seat, etc), or in a holster anywhere but on you, or in a glove box, map pocket, center console box. Or you must have a CWP.
I don't know how many police, sheriffs, or DPS officers actually know case law, or will charge on chase law, as opposed to just reading the statute and applying the law as it was meant to be. You could be taking a crapshoot with your freedom.
Hope this helps.