My understanding is that if you have a permit to carry a concealed weapon in a state, it covers the state. People do this for a large variety of reasons.
Not sure about the laws and the ease of which you can recieve a permit in any state but Maine, but Maine's laws are fairly open to most.
This whole 'weapons vs hiking' vein has been opened and discussed many times.
People have their own views, but this is a hiking website.
If weapons are your thing, get a subscription to 'Small Arms Review' or 'Soldier of Fortune'.
Personally, and this from someone who owns more than one gun, and has inherated several more, some fully auto, I don't see them mixing unless you are hiking in Denali on your own, or in some other desolate unpatrolled place where there are animals that a 45 won't stop.
I have been dropped off by a small plane on a strip of beach that has no name on any map, to fish for salmon. The salmon were so plentiful i could have scooped them out of the water with a net rather than fish for them. And they were so strong that with in a few hours of fishing they had run out and snapped all of our lines. We spent 3 days there after that, waiting for a plane to bring us back. Every night we cooked and ate dinner and stripped and walked 1/4 mile to out sleeping tent.
Every morning we awoke and went to the 'cooking tent' to find that a mama bear and a few of her cubs had gone through our fire pit and scratched at out bear canister. There were tracks all over the beach of very large paws, with frigtheningly large claws, and smaller paw prints, with equally frigtheningly large and sharp looking claws.
Fortunatley for us, we never actually encountered them in person.
Flying back home from this unnamed beach, we did spot a mama bear and two cubs further upstream. Seeing them from the air was wonderful.
Could I have ever shot one? Most likely not for a variety of reasons. The biggest one being I am a really lousy shot and can't hit the broad side of a barn usually. Fortunately the sound would probably have driven them away had we had an encounter.
This was in Alaska, in an unnamed part of country as a fly in only accesiable section of an unnamed beach on a river during salmon season. This is the highest bear activity time near rivers there is in Alaska. We were dependant on weather and the tide for a pick up, as the only place for a plane to land was the beach at low tide, when it was firm enough for a Cessna to land and take off.
I can not imagine a similar situation here in NH that would have me carrying a weapon as those times in Alaska when I did. I did it more for the peace of mind of my dad and my Alaska friends than myself, since i was fairly confident I would not have been able to shoot at a bear, or really, be able to even hit one!