My introduction to skiing in copper country was seeing what looked like moguls (bumps in the snow) moving, as I was going uphill on the ski lift.
It was actually a white Husky, and the owner was in the chair ahead of me. His dog would run uphill when he was on the lift, meet him at the top, then turn around and run downhill. Not only would the dog run quicker than his owner skied, (and this is super steep so you ski downhill really fast) but the dog picked better lines than the skier, too. As the evening went on the dog stopped running all the way to the top, and no longer could keep up with the skier going downhill, either; but he never stopped running.
The intelligence of the animal to navigate this was really impressive, not to mention his ability to stay out of the way of other skiers. There's no way the owner trained the dog to do this, but he did have to exert control to prevent the dog from running itself to death.
It was also really cool that the facility let them do this. It was a great introduction to a beautiful part of the world. I've also seen people skijoring across flat-ish ground, which is basically using your dog to pull you as you cross country ski. They use a specialized spring loaded tow rope to avoid too much shock to the dog, evening out the weight they pull.
Dogs doing anything like that are really happy! Dogs will always be happier when you spend a lot of time with them, developing a good relationship