The state's definition of "deadly weapon" is incredibly vague and count potentially be applied to any sharp object. It does not explicitly say any sort of folder is illegal. It just uses language that could be applied to them, or any other knife. That said, the culture of New Mexico is likely to be a bit more lenient on knives than say, New York. If you're minding your own business, you're not likely to be searched, much less charged for a pocketknife.
Obligatory Statute Dump (truncated for brevity):
A. "great bodily harm" means an injury to the person which creates a high probability of death; or which causes serious disfigurement; or which results in permanent or protracted loss or impairment of the function of any member or organ of the body;
B. "deadly weapon" means any firearm, whether loaded or unloaded; or any weapon which is capable of producing death or great bodily harm, including but not restricted to any types of daggers, brass knuckles, switchblade knives, bowie knives, poniards, butcher knives, dirk knives and all such weapons with which dangerous cuts can be given, or with which dangerous thrusts can be inflicted, including swordcanes, and any kind of sharp pointed canes, also slingshots, slung shots, bludgeons; or any other weapons with which dangerous wounds can be inflicted;30-7-1. "Carrying a deadly weapon".
"Carrying a deadly weapon" means being armed with a deadly weapon by having it on the person, or in close proximity thereto, so that the weapon is readily accessible for use.30-7-2. Unlawful carrying of a deadly weapon.
A. Unlawful carrying of a deadly weapon consists of carrying a concealed loaded firearm or any other type of deadly weapon anywhere, except in the following cases:
(1) in the person's residence or on real property belonging to him as owner, lessee, tenant or licensee;B. Nothing in this section shall be construed to prevent the carrying of any unloaded firearm.
(2) in a private automobile or other private means of conveyance, for lawful protection of the person's or another's person or property;
(5) by a person in possession of a valid concealed handgun license issued to him by the department of public safety pursuant to the provisions of the Concealed Handgun Carry Act [29-19-1 NMSA 1978].
C. Whoever commits unlawful carrying of a deadly weapon is guilty of a petty misdemeanor.Sources:30-7-8. Unlawful possession of switchblades.
Unlawful possession of switchblades consists of any person, either manufacturing, causing to be manufactured, possessing, displaying, offering, selling, lending, giving away or purchasing any knife which has a blade which opens automatically by hand pressure applied to a button, spring or other device in the handle of the knife, or any knife having a blade which opens or falls or is ejected into position by the force of gravity or by any outward or centrifugal thrust or movement.
Whoever commits unlawful possession of switchblades is guilty of a petty misdemeanor.