Today President Obama designated the Organ Mountains-Desert Peaks region near Las Cruces, NM to be a National Monument. The 500,000 acre area includes mountain, desert and grassland habitats as well has archeological and historical resources. There are numerous petroglyph sites and the Butterfield Stage route passed through the area. Several rare plant and animal species also call the area home. There are hiking, biking and horse trails but currently I was unable to find any information about regulations for pets.
Here is a link to the website: Organ Mountains. When I get some photos and some information about pet regulations I will update this post. If any of my readers are in that area and can find out if there are any pet friendly trails please post the information in the comment section.
Update for Organ Mountains-Desert Peaks
April 26, 2017, Trump signed an executive order to eliminate or reduce the size of this monument. Although the 60 day comment period has now ended, more than 97,000 comments were received in support of the monument. Local officials recognized that the Organ Mountains-Desert Peaks National Monument is an economic boom for the local communities and have passed formal resolutions to support it.