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"Hike your own goddamn hike" Depends on your what you are trying to accomplish outdoors. A hunter and an Appalachian thru hiker have very different objectives, thus different gear. If you're hiking a multi-day trail I don't recommend an axe, infact depending on the climate you may only want a folder (though I simply prefer 4"-6" fixed blade, weight vs capability wise).
If you're hunting from a base camp though, especially in the North during opening day, an axe or hatchet can be an invaluable tool. Breaking branches between 2 trees, batoning, beaver chewing, bending and slicing, etc are all great things to know how to do and I have done all of these myself in confidence.
But if you can take the weight, what's a more effective tool for processing firewood? A felling axe or a Mora? Obviously if weight isn't as important you choose the equipment accordingly that you prefer. For me, usually my old Marttini knife and my Estwing 14in hatchet or Bahco/Corona folding saw. Occasionally a Cold Steel SRK or an Ontario SP8(which is in my truck 'urvryday), RAK, or USAF knife will replace those.
It's all about enjoying the recreation after all.