I have a GB small forest axe that I carry in my 72hr kit, and a full size axe in each of my trucks. A good axe is priceless for building a natural shelter, fire reflector, and many other outdoor needs. I'd much rather have a 4-5" bladed knife and a 19" handled axe than just a big knife.
That said, I don't see packing an axe on a hunting trip when I don't plan to do any of those things. To my way of thinking a good lightweight tarp or other pre-made shelter is lighter, more waterproof, and takes much less energy than building a natural shelter. I pack my 11oz Kifaru Paratarp in my hunting kit along with 9 aluminum stakes, 50ft of paracord, and 30yds of trotline cord for about 18oz. I figure I can't pack much of an axe or even a heavy knife and sheath for that weight. I pack either my SOG Revolver or Buck crosslock that have small but funtional saws if I need to process small amounts of wood. I also pack a emergency bivy sack for sleeping and a cheap mylar space blanket that can be used as a ground sheet or fire reflector.
I guess if I was planning to head out into the wilderness for long term survival I'd definitely want an axe. I just don't see packing the weight hunting when I already have plenty to carry. The places I have hunted there has always been enough dead wood between dry limbs/trees and dead stuff on the ground to keep a campfire going for a night or two without needing an axe to process wood. I may feel differently if I was hunting somewhere that wasn't the case.
