Isn’t New Mexico an open carry state?
Do people who open carry also have to have a concealed carry permit?
In New Mexico, no you do not have to have a permit to carry open. A permit is required for concealed. The rules are different with respect to carry type (primarily with respect to alcohol selling establishments and school zones). I wish we'd adopt our next-door neighbor's (AZ) laws with respect to that.
Why yes, yes it is.
Constitution of New Mexico, Art II, Sec. 6. [Right to bear arms.]
No law shall abridge the right of the citizen to keep and bear arms for security and defense, for lawful hunting and recreational use and for other lawful purposes, but nothing herein shall be held to permit the carrying of concealed weapons. No municipality or county shall regulate, in any way, an incident of the right to keep and bear arms.
Do people who open carry also have to have a concealed carry permit?
Nope. The Michigan thing was an interesting legalism, the federal no-guns-on-school-property law allows for certain people who have a permit to carry in schools, so long as it is plain sight, the Michigan CCW permit qualified as one of the permits so the man's conceal-carry permit made it legal for all of his actions.