Desert Dweller:
Actually, The State of New Mexico Currently Enjoys Constitutional Carry of an Unloaded Firearm.
New Mexico only Prohibits going Armed with a Firearm that is BOTH: 1. Concealed, AND 2. Loaded.
Open Carry is Legal, regardless as to whether a Firearm is Loaded or not.
Concealed Carry without a Permit is also Legal so as long as The Firearm is Unloaded.
Therefore, anyone at least 19 Years Old can Carry a Handgun, Openly or Concealed, whether on Foot or in a Motor Vehicle, so as long as The Handgun is Unloaded.
As a Reference, Please Refer to NMSA 30-7-2(B), here:
http://public.nmcompcomm.us/nmpublic/gateway.dll/?f=templates&fn=default.htm
However, there is NO Unloaded Open Carry Allowed on The Premises of any: 1. School, 2. University, or 3. Licensed Premises which may Serve or Sell Liquor.
Furthermore, it is Unlawful in New Mexico to Carry a Firearm Aboard a Bus with a Seating Capacity in Excess of 15 Persons.