You'd ask a lot from a dog, but not the impossible. However, there's no magical dog breed that will happily do all these things on their own without training and guidance from you.
If you stay at home 11 months of the year and then travel for one month, the sudden change will cause enormous stress for your dog. It would be better to leave them at a friend's house, a dog hotel or boarding kennel for the time. If you're always on a road trip, take your dog with you from day 1 to get them used to the lifestyle.
For a sturdy dog that does well in many different climates, I would look for any of the many guard dog breeds that originated in mountain regions (there are a lot). Mixed breeds are just as suited as (maybe even more so than) a pure breed. I would avoid breeds that:
- Have very little or very short hair. Although you can put them in a coat in cold climates, their legs and paws are still vulnerable and the hair also protects them from heat.
- Are bred to participate in breeders contests. In the last 100 years, breeders haven't had the dogs well-being and work performance in mind, but mostly their looks. That led to some medical problems like hip dysplasia in German Shepherd Dogs and chronic difficulty breathing in French Bulldogs.
- Require constant hair care. Poodles are actually a healthy and sturdy breed, but their coat won't stop growing. You must groom them in regular intervals, which might not be suitable for your plans. Other breeds have such a thick and long coat that they are prone to matting and need to be brushed regularly.
Speaking of grooming... A very sudden change in daylight duration and temperature can trigger a very sudden coat shedding in a dog. Some people that moved from one climate zone to another report that their dogs had extreme seasonal sheds that sometimes resulted in matting a few weeks after the move.
Another problem is acclimatization. If your dog lives in a temperate climate 11 months of the year and in a dry home during rain or snow, you cannot expect them to suddenly do well in arctic climates or a rain forest. The dog's whole body, including fur, skin and metabolism, has to adapt to the climate. Dogs who always "live rough" are adapted to many different temperatures and weather conditions, but dogs who live a sheltered life with their humans will struggle.
The same goes for walking or swimming. Any dog can swim (and walk), but you cannot expect them to run a marathon and cross a river with you if you never trained such lengthy activity with them. Dogs suffer from exhaustion and sore muscles just like humans do.
And please don't forget to get your dog vaccinated and preventively treated for parasites.
Apart from those biological issues, there are also social issues. You'll need to get your dog used to traveling, different people and places from a very young age.
You'll probably also need to get them used to:
- Wearing a muzzle and leash.
- Being in a travel container.
- Being handled by different people.
- Riding in different types of vehicles like cars, trains or boats.
- Not approach any strangers. There are cultures where dogs are seen as dirty animals and people won't want them near them. There are also people who are afraid of dogs. You must train your own to leave people alone.
- Not hunt wildlife. If you're on a trip and your dog dashes after a wild animal, it could be lethal if the animal is poisonous, defends itself or if your dog gets lost.
These things don't happen on their own. You must expose your dog to various situations like these early in their life (preferably before 4 - 5 months of age, as that is the "socialization" phase of their life that shapes their character).
Side note: the breed of a dog does not define their personality. You'd probably want a "socially motivated dog" as described in this post for a travel companion. Other dog personalities are also suited for traveling, but for the socially motivated ones home is where you are.