I guess since nobody has answered I must be the closest one that's read the post. I've never heard anybody talk about riding around silver city.
I went to the Gila National Forest web site (http://www2.srs.fs.fed.us/r3/gila/faq/#1) and here's what they say: Off-Highway Vehicle (OHV) recreation, including ATV and motorcycle use, is just one of the many uses allowed on National Forest lands. For reasons of erosion control, we ask that they be kept on existing roads. It is your responsibility to know and abide by regulations relating to motor vehicle travel. State law requires registration of all motor vehicles before being operated on public lands. Federal law (36 CFR 261.16(a)) prohibits operation of any mechanical or motorized equipment within the boundaries of a Wilderness.
I take that to mean you gotta have an off-road registered vehicle but I could be wrong.