"People have been free to carry a loaded gun openly in NH since statehood. That is to say, there’s never been a law that prohibits or regulates it."
Caveat- carrying in a vehicle requires a permit.
In Vermont since before statehood:
"The Vermont Constitution of 1777, dating well before the Bill of Rights to a time when Vermont was an independent republic...."
In the modern era, the Vermont Supreme Court established the right to carry firearms without a permit in State v Rosenthal, 75 Vt. 295 (1903).