I live 40 miles SW of Yeso so I am very familiar with the area you are inquiring about. I suspect SE N.M is quite abit more conservative than the part Professor Marvel hails from and I say that because I am a lifelong resident of this area and I have only seen open carry in town (Roswell) on only two separate occasions. I have never seen anyone open carrying in Ft. Sumner, Carrizozo, Capitan, Vaughn.... besides the law, of course.
I'll add, even though I know few people there, these are small rural communities and everybody knows everybody for miles and miles around. The odds of being robbed are extraordinary high.
I'm sure open carry is seen more often in the small towns in the brushy / timbered areas during hunting season.
New Mexico is a very friendly gun carry state and has had legal open carry since the establishment of the territory. Years ago the Supreme Court ruled that your automobile is an extension of your home and I always "figured" that about 80% of the traveling residents had some sort of firearm in the vehicle.
CC has caught on like wildfire and a number of years ago an adjoining ranch neighbor put on a CC class at his ranch which pulled in lots of people from a 60 mile radius. I suspect that is how most New Mexicans are packing their iron.
But, guns in the ranch country are probably more common than shovels and are discussed about the same.
As the Professor says, "Yes, we like it in N.M.
A lot".
Billy