I don't feel a *need* to carry a weapon while camping but I do choose to carry one all the time. I'm speaking of a handgun of course, a Springfield XD45 Compact to be specific. I grew up around guns. They were just a tool like any other. A fun tool to practice with, but just another tool. I applied for my concealed carry permit on my 21st birthday and have carried every day since it was issued 30 days later. In 24 years of daily carry my weapon has only saved my life once. The one and only time I've ever pointed a gun at anyone it was a guy about to smash my head in with a pair of bolt cutters. I'm damned glad I didn't have to pull the trigger, but even so I couldn't sleep or eat for more than 48 hours afterwards. Apparently staring Death in the face can have that effect.
Back to the real topic at hand. I have a house and property that borders an extremely brush-choked State Forest with a bunch of off road opportunities. I started out carrying a Walther PPK/S in .380ACP and always felt that with my training and marksmanship it was plenty for two legged predators. I carried it for 17 years and it's the gun I drew on the tweaker with the bolt cutters. After seeing a large cougar in our yard at the house in the forest a couple times I called the game warden. He came out to meet with us and give us some pointers. Take down the bird feeders, play a radio outside 24/7, cut the brush back further, etc. His biggest recommendation was to get a larger caliber carry gun. I asked him what he carried and if he got to choose it. He said their whole department is allowed to carry whatever they want and everyone carries .45s with +P self defense rounds intended for use on humans. The reasoning: Other than humans Cougars are the number one threat these guys face. Cougars are lean, muscular, thin skinned mammals that range from 75~350 pounds. In short, they are very much like humans in anatomy so whatever works good on humans works good on cougars. He personally had killed three cougars in the bush with his sidearm in the line of duty. Two were charging him, the third was charging another warden. Cougars do NOT mock charge. When startled (typically if they're sleeping or occupied stalking something) their instinct is straight up attack, not flee. If they hear you coming or know where you are you will likely never see them and they'll slink away silently. The warden said if you ever see a cougar kitten in the wild you're already dead! So I bought a .45 and some +P HSTs for carry on his recommendation. I got even more training as well, and started going shooting weekly instead of monthly. Doing short range trips to shoot 150-200 rounds rather than going out in the woods for a whole day of shooting all my guns.
I always have my .45 on my person, I carry it IWB with a reload the same way on my weak side. Nobody ever knows it's there unless I want them to know. I recommend that anyone that wants to be armed in the woods start with a handgun. A shotgun in your tent or truck is useless if the threat is between you and it, or the threat is a large animal and you can't really move or have to gather your kids. The great thing about a carried handgun is it's always there and you can use it with one hand up to and including at contact distance while you're being attacked. Anytime I'm going into the woods my Saiga .308 goes in the truck. I don't imagine I'll ever have a need for it but when you own a tool like that it seems silly to go someplace remote with large wild animals and sketchy humans and not bring it along. I built it with an Ace folding stock so it's very compact to store and is fully functional with the stock folded or extended. If I ever had to hike out of the woods the Saiga would be locked and loaded and slung on my back in case of bear problems. Guess I do have a valid reason to carry it in the truck.

A friend from Alaska says "People who carry bear spray up here end up being grizzly poop." He carries a S&W 460V on his hip whenever he's in the woods and slings a rifle when it doesn't impact his activities too much.