Vermont doesn't "recognize" a TN permit. Anybody with no criminal record can pack in VT without a permit, period, doesn't matter what state they're from.
AZ will be the same way. Visitors from Cali or wherever will be able to pack.
Green card holders too, from wherever.
LEGAL visitors from other nations, I'm not sure about to be honest. They can't buy guns per fed rules, but I don't know if it would be legal for them to borrow one. I intend to find out. It would be kinda cool to have a visiting friend from England realize that the whole place is basically awash in guns, and offer them a loaner
.