N.M. Code R. § 19.2.19.14
A recreational access permit does not grant a right to enter upon or cross lands not under the control of the commissioner. Also, a recreational access permit does not grant a right to access lands by motorized vehicle. The use of motorized vehicles or any mechanical form of transportation for recreational access is restricted to public highways and roads, as defined by Section 67-2-1 NMSA 1978, and to established roads that cross the lands to which access is granted under the recreational access permit. When lands open to recreational access are fenced, vehicle access is allowed only where there is an unlocked gate that can be accessed from an immediately adjacent public highway or road, or from an immediately adjacent established road that crosses the lands to which access is granted. When a recreational access permittee opens an unlocked gate to gain access to lands by motorized vehicle, the permittee must close the gate after passing through. Where there is no such access through an unlocked gate in the fence, recreational access beyond the fence shall be limited to travel by foot.
N.M. Code R. § 19.2.19.14