So what are the laws on open & concealed carry? Any list of state CCW's they recognize?

I'll have to look that up, Stu.
NM is an open carry state, and It's not been an issue before. Anyone can carry openly.

Stu, looks like you're out of luck. For whatever reason, NM doesn't honor Alabama CC permits. This according to handgunlaw.us

http://www.handgunlaw.us/states/newmexico.pdf

If it's any consolation, AL doesn't honor NM permits either.

As Barry said though, you can open carry in many places. So you can pack your pistol around on your belt while hunting or running around town. However, the normal places (Post Offices, fed buildings, state buildings, schools, etc.) are off limits. Of interest - no carrying in establishments that serve alcohol for consumption on the premises.

so I need an open carry gun & a concealed carry gun

Stu, everyone needs an excuse for another gun !!!
Mark

Open carry for handguns - legal, but not real often done.

If your jacket covers the firearm, violation - now concealed.

You can have a firearm ANYWHERE and in ANY CONDITION in your vehicle. Vehicle is considered an extension of your domicile (home).

State permits recognized by New Mexico - from DPS website
Alaska Kentucky North Carolina Tennessee, Arizona Michigan North Dakota Texas,
Colorado Minnesota Ohio Utah, Delaware Missouri Oklahoma Virginia, Florida Montana South Carolina Wyoming

One gun - two holsters!