In New Mexico yes, most of the state is public lands available for hunting on.
Follow this link and you can get much info about them on the BLM website. http://www.blm.gov/nm/st/en/prog/recreation/las_cruces.html
Follow this link and you can get much info about them on the BLM website. http://www.blm.gov/nm/st/en/prog/recreation/las_cruces.html