If I'm in the woods I generally have a sidearm. If I'm big game hunting that sidearm needs to be big-game legal, otherwise it's just a signalling device, rather than a back-up gun.
Sure a .30-06 packs more whallop than a .44 mag, however I had a day where I was packing out a quartered elk, and ran smack dab into a cow elk at 10 feet away. All I had on me was a 22 pistol. Not legal, nor ethical to try and drop an elk with a 22, so next season I bought a .44.
The next thing I knew everyone in camp had a .44. Well, just call me a trendsetter.
Seriously, even when grouse and turkey hunting I usually have a pistol of some sort, and thanks to running into a bear at close quarters, armed only with a shotgun and a .22 pistol, it's a .357 or bigger.
Colorado allows open carry for self protection (even if you aren't hunting) as long as the firearm is not concealed. Hence, I have a fishing/backpacking gun too.