One quick note, under the new law, you can carry a loaded handgun
in your car
Rifles and shotguns must be "Utah unloaded" (IE no round in the chamber, but a fully charged magazine is ok) unless you have a permit to carry.
Any lawfully possessed gun may be carried either openly or concealed on or in the vehicle.
76-10-505. Carrying loaded firearm in vehicle or on street.
(1) Unless otherwise authorized by law, a person may not carry a loaded firearm:
(a) in or on a vehicle, unless:
(i) the vehicle is in the person's lawful possession; or
(ii) the person is carrying the loaded firearm in a vehicle with the consent of the person lawfully in possession of the vehicle;
(b) on a public street; or
(c) in a posted prohibited area.
(2) Subsection (1)(a) does not apply to a minor under 18 years of age, since a minor under 18 years of age may not carry a loaded firearm in or on a vehicle.
(3) Notwithstanding Subsection (1)(a)(i) and (ii), a person may not possess a loaded rifle, shotgun, or muzzle-loading rifle in a vehicle.
(4) A violation of this section is a class B misdemeanor.