A few months back someone in the CHL department got a wild hair and basically said "no reciprocity" completely out of the blue. That statement did not go over well with the gun carrying public in NM. The statements were redacted less than 3 hours after being made, to the tune of (what I imagine to be) several thousand phone calls to the CHL office. When I called to clarify the original statement the lady that answered my call sounded completely exhausted.
Suffice it to say you'll be fine. Enjoy your trip.
Have your heater when things get really cold.