I am a Canadian citizen soon to be living in the USA. I have checked the laws for New mexico, and it seems they only offer CCW permits to US citizens. However I have looked up the reciprocity, and it seems that if I were to get a Florida CCW, which issues to non-citizens, that I could then carry in New Mexico. Is my thinking correct?
While some states do, indeed, issue CHL's to non-residents who live in other states, it'll depend on whether your state of residency (NM) recognizes such non-res CHL's from those states. I don't know NM's particulars, but some states require that in order to recognize another state's CHL that the person must be a resident of that state; ie, no non-res permits from that state are recognized. Again, I don't know for certain about NM's specific reciprocity agreements with other states, but you'll want to check on that, and whether they'll recognize a non-res license.
And some of those states who do issue non-res licenses change their requirements from time to time. Utah, for example, has previously been a big non-res issuer to non-Utah folks. But just this past year, Utah required folks in CHL states to first have CHL's from their own state of residency prior to issuing a non-res CHL to that person. And, as I said, some states only recognize "real" CHL's, not non-res ones, specifically to disallow its own citizens from acquiring a CHL of another state despite not qualifying (or not pursuing) a CHL in their resident state.
Confusing, a bit. But, check the reciprocity and non-res acknowledgment specs for NM, and what they require for issuance of CHL's (ie, whether they'll do so to non-citizens).
Good luck on the move.