We've used guns as noise makers to scare grizzlys off while fishing in alaska. I carry one often when riding in remote areas. But I'm not too worried about needing if for animals. Although I wouldn't hesitate to fire it. But unless I was seriously threatened I wouldn't fire to harm but rather to scare.
I have had horses get hurt and die in the back country. It's no fun to cut a horses throat with a knife because he needs to be put down. You only need a permit if you concel the weapon. It's bad enough to have to take your saddle and cut the brand off your old friend when they go down. Utah allows you to carry pistols out in the open with out a permit. I just put a holster on my belt.
The law was changed about carrying guns in national parks like Yellowstone. But I don't think it has taken effect yet. I know congress passed the law, but the liberals got a time delay, I think it goes into effect this year. I know I was suprised last summer in Yellowstone, I had heard about the new law, but the rangers promptly straighten out my understanding that I couldn't carry a gun last summer in the park.