Dogs are a touchy subject because they become very Personal pets. I rarely if ever bring dogs, because generally where I am going is up cliffish stuff quite often and dogs don't have opposable thumbs able to repel very well…
2 types of dogs. 1) city in door dogs who are never let loose and are out of shape and also have no fur coat as they are kept in doors and 2) country dogs who are let free to roam and left outside. IF country dog sits in sun all day and is old, then they will also be out of shape, but if young and it wanders is fine.
Dogs who are country dogs, you don't have to worry about their paws. You don't have to worry about their fur coat warmth either. Our dog sleeps in the snow every time it snows instead its straw filled house. Yes, it depends on the dog. Any sheppard/collie like dog with longer fur has no problems with cold. If you bring a small tent for the dog they will go in. Even short haired dogs if country reared will have a high metabolism and snow is fine for them. But if camping on snow, still bring a pad for them as usually they will have their summer coat by then instead of their winter coat.
City dogs are stupid and should be kept on a leash all the time as they don't have a clue what a deer is, what a coon is, what a porcupine is, what a bear is, what a bobcat is, what a cougar is and will go bounding off yapping away and possibly get lost because they have never learned. A country dog, may yap, but won't get lost, and if unfamiliar territory won't go wandering off either.
Dogs in unfamiliar territory will "protect" their person, but not the "area" unless there are more than 1 dog present and form a pack.
If you want peace of mind with a dog, DO NOT BRING 2 dogs! 2 dogs = they will wander, aka PACK mentality. Likewise don't bring YOUNG dogs. Old dogs = peaceful dogs.
Dogs, won't fight in unfamiliar territory. They will growl and sniff, otherwise nothing more unless if someone brings a "pack" of dogs. IE more than 2. Even then dogs are far smarter than people and won't fight. Only scardy cat fearful humans do you have to worry about and their interaction with dogs.
If you come in contact with a group of people with 2 dogs and you have a single dog, the best thing you can do is to let the dogs figure out who is boss ASAP and everything will be fine from there as they are yapping about who is dominant. If that poster up-thread had bothered to let his dog loose he wouldn't have had to "kick" the other dog at all. The dogs would have sorted everything themselves. Yea, your dog might have gotten humiliated, deal with it. That is how dogs work. If you don't understand how dog pack dominance works then you will post long idiotic rants like the poster up-thread.
Learn how dog packs work and your life will be far simpler.
PS. I never have my dog anywhere near where I sleep. They stink and are hairy monsters. Especially when wet. Either have them sleep outside or tie them to the good ol' common mountain hemlocks that are very dense and low growing if it rains. Lets be real here, it its raining your probably not going hiking to start with. Nearly everyone goes hiking in the summer where at most you get 1 day of rain. More likely is afternoon thunderstorm. Dog is fine in that. Humans are fine as well. Just most of us are city slicker 72F indoor pansies.
PPS. Bears etc will RUN from a yapping dog. Even a tiny one. Especially if there are 2. Built in instinct. The idiot up thread who posted they would bring a bear back is truly ignorant of why nearly all country folk HAVE a dog not leashed to start with. Dogs are a far better defense against bears than even a gun as a Bear Fears a dog, not a gun.
PPPS. To the yokel who said dogs can't carry weight. Are you for real? Dogs have been carrying weight throughout the ages. They do need to be in shape though.
PPPPS. Its not unheard of for a dog pack to move 50-100 miles a day. Our neighbors had a German Shepard making daily "excersice" jaunts to his lady friend 25 miles away for a total 50 mile round trip. They found out when they finally captured their tagged dog in said persons fenced in yard several times.