On April 27, 2012, the New Mexico DPS decided that the Texas CHL requirements were not “substantially similar” to the New Mexico Concealed Carry requirements. This decision is subject to review, but as of now, the Texas CHL is not recognized in New Mexico.
New Mexico does allow unlicensed carry of a firearm in a motor vehicle, subject to restrictions, and also allows open carry in some public locations, also subject to restrictions. However, a Texas CHL holder may not carry concealed at this time in New Mexico.
As with any other state, if you are taking a firearm into New Mexico, you need to make sure that you know and understand the rules of that state. Remember that once you leave the state of Texas, you are under somebody else’s rules, and the rules and regulations that you learned in your Texas CHL class may be different in several important ways — and that the Texas CHL instructors may not be familiar with those differences.
Here is a link to the New Mexico Concealed DPS page on Concealed Carry. From my quick reading of the reciprocity criteria that they list, the most probable cause of the decision to drop reciprocity appears to be that Texas will issue Concealed Carry Licenses to legal resident aliens, and New Mexico does not.
UPDATE: The NM DPS has announced that they are again recognizing the Texas CHL, as of today (May 2nd). However, you should carefully check the NM DPS website before carrying a firearm there. We have just seen that the situation could change overnight.