What's the deal with open carry in new mexico? Specificly santa fe?

Going to be doing a short road trip and santa fe is one of my stops. I always bring a hand gun with me when I am traveling long distance. Arizona is a constitutional carry state so as I understand it anyone over 21 who can legally possess a firearm can carry it concealed. But I know new mexico is not as lenient with its regulations but still has open carry. So is it normal to see people carry openly or best to just keep said firearm in the car/hotel if i need to make a stop as to not make anyone freak out? And secondly is it legal for a loaded firearm to be transported in the car through new mexico as well?