Yes Mt honors your permit http://www.handgunlaw.us/LicMaps/ccwmap.php
As far as I know you can carry at the air port as long as you stay in the areas not secure: like thebaggage 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.