I have never felt the need to carry in the woods of Colorado unless I am hunting. If I am hunting then the extra weight of a sidearm is a waste of my energy. Carry if it makes you feel safer.
I think BeanMan has the right idea.
I went on my first wilderness backpack trip in 1958. I've probably gone on an average of 5 or 6 per year, every year, since then. So that makes several hundred trips into the wilderness. Two or three times that many nights and days.
I have never been threatened by man or beast in the backcountry. I own a Ruger SP101 .357mag. Lots of people say it's a great concealed carry revolver. But I never carry it when backpacking or hiking in the wilderness. Too heavy. Not worth the effort. There are some places in inner cities where I might carry it. But not in the outdoors.
I have carried my Ruger Blackhawk .357mag instead of a rifle, when returning to retrieve the remainder of a carcass.
KC