I use dogs for many things but when they are with me in the mountains they serve two main functions. When I turn my horses and mules loose to graze they watch them and keep them close to camp. When I have an equine escape artist they fetch him up and bring him back.
When we are riding down the trail the dogs range around me and let me know if anything or anyone is around. In my camps the are just kind of there but that is enough to keep the bears and big cats away from my camp and my livestock.
This is what I raise and work. they were one of the original WWI military working dogs and they are very good working stock dogs.
http://www.puppyshop.com/caninebreeds/blgnshpdog.htm I've also trained them for tracking, scouting and as search dogs.
I know we all agree on many things about Mr Kim. This guy had courage, and he went to the very end in an attempt to save his family. He gave it everything he had and then some. This is a fact that no one can contest.
Back to the dogs. I've hunted behind many different dogs but it isn't what I prefer. I much prefer the quiet stalk with my bow. It isn't nearly as effective but it's a lot more fun.
Horses and mules.
Sounds like you don't go with just a horse for yourself and one mule.
What do you guys hunt out there? Deer, Elk? I would assume bear.
Some of the fellows I know ride mules because they consider them safer in the mountains.
I have never ridden a mule. And I would add that if my horse can't go there safely, not to worry. I don't want to go there anyway.
I have also heard that a horse you ride in the mountains is safer without shoes. There again, I have no experience. All of the horses I have ever owned had to be shod. Of course, the Mustang has a much better foot that the TB.