You can carry open or concealed as long as you are in your car. Open carry is allowed outside your car, except in places selling/serving alcohol, public buildings, schools, etc. If a business posts a "no firearms sign", respect it. You can carry your firearm unloaded along with a loaded magazine in a concealed fashion -- above restrictions still apply. That is the 20 cent tour of New Mexico laws. Further, more detailed info is available on this site.