New Mexico does recognize the Arizona CCW Permit for non-residents visiting their state.  

The biggest thing to remember when carrying on a non-resident permit is that you must abide by the laws of the state you are visiting, not the state where your permit was issued.  This means you are responsible for knowing New Mexico law when carrying a firearm there.

Fortunately, many of the laws in New Mexico are similar to those in Arizona.  Open Carry is unrestricted in most public areas and seems to be generally accepted.  Also, like Arizona, New Mexico is a ‘shall issue’ state.

Carry of a concealed weapon by a person on foot requires that they have a concealed weapons permit.  Vehicle carry of a firearm in New Mexico is unrestricted.  Persons may carry a loaded firearm, concealed anywhere in their vehicle without a permit as long as the firearm is being carried for lawful self defense.  The firearm can even be placed in a purse or briefcase, as long as it stays inside the vehicle while being concealed.

Firearms are prohibited in posted areas or other locations such as game preserves, schools, courthouses, national parks, federal office buildings and any establishment where alcohol is served for consumption on the premises.  

Carrying a concealed weapon into a place that serves alcohol is a 4th degree felony…so I’d take special care to avoid breaking that law.

Other information regarding concealed carry in New Mexico can be found at the New Mexico Department of Public Safety website:

http://www.dps.nm.org/lawEnforcement/ccw/index.php