As far as I know you can carry at the air port as long as you stay in the areas not secure: like the baggage claim.
I used to live in great falls for about 7 years 4 years ago. didn't get a chance to OC or CC, not as involved then as I am now. I doubt you will have problems.
Great Falls MT is my favorite airport. I went through there one time on a trip from Seattle, WA to my home in Wisconsin. Tiniest, coziest little airport I've ever seen.