So this thread seems to be wandering from self reliance to survival and back again. I've never really been sure at what point things go from one to the other, or specifically when someone is in a "survival situation", and when they're just doing chores like fixing a broken part while staying warm, dry, and hydrated in a manner or place they didn't expect when they got up that morning. I once read about a guy who was asleep in the back of a WWII bomber on a training mission over Yellowstone Park. He was awoken by the bail-out alarm, and thirty seconds later he was on the ground, at night, in the winter, 60 years before PLB's were even dreamed of. I recon HE was in a survival situation. I think most other folks are just doing chores.
MTV: apologies if I misread your attitude towards the subject, but this has the smell of something that can be argued to infinity without resolution, and I'm not interested in going there. I'm also not qualified to state whether there's a temperature at which axes become ineffective, but I
suspect there is not...less effective for sure, but not ineffective. I do know that people have been using axes in the far north for as long as people have had axes in the far north, and saws are a comparatively recent advent. It wasn't until the late 1800's that steel mills were able to make quality saws for the consumer market, and they were prohibitively expensive for most people until well after WWI. And even then they were all but useless to a bushman who couldn't also afford the joiner, files, setters and a saw vice to keep it working, and had the knowledge to do the pointing, sharpening, and setting. The historical literature on axes doesn't make mention of a point at which wood cannot be chopped, but it does regularly mention warming your axe under your coat before starting to chop in very cold temperatures. Regardless...very few people are operating their Cessna's and Piper's at -35 degrees, and if they are, they damn well better not be getting their advice off a internet forum, no matter how good it might be.
I have a fairly exhaustive article on axes that will eventually be published, but here's the readers digest version. The fact that this is the readers digest version tells you something about how over-written the article is...
In a nutshell, my experience is that axes are much more efficient than handsaws or any other hand tool at cutting fire wood and harvesting tinder, and much more versatile as well. I've use both extensively and believe they compliment each other like salt and pepper, but the axe is superior for pretty much everything other than cutting firewood to stove-length. A lot of people have the opposite view, and I think a large part of that is because a handsaw comes from the hardware store in perfect cutting condition and requires about five minutes of use to master, at least for non-binding cuts, while an axe comes from the store in a condition suited to nothing other than splitting cordwood, and requires many, many hours of practice before its potential can be realized. I'm far from anything special with an axe, but with a proper small axe I can pretty consistently double the amount of firewood produced by someone with a sharp 18" hand saw. And a person with an axe can be productive where a person armed with only a saw simply cannot.
A couple simple examples: In an extended rain there can be no dry wood or tinder available, but the wood two or three inches deep in a standing dead tree is virtually always dry enough to light from a match. Accessing this wood is all but impossible without an axe, and incredibly simple with one. Likewise, a person with a saw and a knife can get a handful of fatwood shavings out of a blowdown tree, while a person with an axe can get a shirtfull of fatwood chunks in the same amount of time. A person on a beach or gravel bar where the only readily available wood is a large drift log can get as much firewood as they want with an axe...and practically no firewood without one.
If a tree falls across the strip after you've landed, an axe will clear it, regardless of size. A hand saw will not. An axe can chop through ice to get drinking water, or carve a snow shovel for the building of a snow cave. That chore is made easier with the addition of a saw, but it can be done with an axe alone if need be. It cannot be done with a saw alone.
An axe can cut wedges, and with enough wedges any piece wood can be split, whether for firewood or for lumber. A person with a mallet and knife can also cut and drive wedges, but cutting wedges with a knife is so inefficient as to change it from a reasonable chore to an arduous one. The same is true for cutting and driving stakes for tie-downs or pickets...I prefer to cut stakes with a saw because it gives a nice flat head to pound on, but in the time it takes to sharpen one stake to a point with a knife I can sharpen ten to a point with an axe. To each their own, but carrying a rather limited tool like a mallet instead of a very versatile tool like an axe doesn't make any sense to me at all.
Perhaps most importantly, an axe can be kept in top cutting condition in the field, while a saw cannot. Saws will stay sharp for a very long time if they cut only clean wood and are never pinched in a cut, but just a few cuts across a piece of sand impregnated driftwood and most of the efficiency of a saw is gone. It'll still cut, but not well...not fast. It just wears through wood like a skinny file. That piece of driftwood will dull an axe too, but the axe can be made shaving sharp again in minutes. A dull axe is just a tool that needs some attention, while a dull saw is about as useless as a piece of steel can possibly be.
There's no question that saws are safer. There's also no question that a large saw made for cutting timber is more efficient than an axe, but you can't cut timber with a saw for any length of time without also having an axe to limb, debark, carve and drive wedges, chop out binds, etc.. The reverse is not true...an axe as a stand-alone tool is unmatched for its versatility and productivity.
It takes skill to use and care for an axe...much more than it takes to cut arm-thick branches with a hand saw until its dull and then buy another one. But a person who learns how to chop well (which includes understanding timber) can literally use that one tool to turn a tree into anything they can imagine. Efficiently, safely, and quickly. That's the key to the city, at least where trees grow.
Here's a link to one of my favorite axmanship films. It's not very relevant to what a pilot might need to do, but it's a great film on many levels, and it shows what a person with an axe can do. Anyone who watches it and isn't gob-smacked by the quality of the axemanship hasn't swung an axe enough to know up from down. These guys are to a double-bit axe what Bob Hoover was to a Twin Commander.
Enjoy!
https://www.youtube.com/watch?v=fc0mdjknbPM
, and in ten years I've yet to see anyone change your mind on something.
. But, I'm on a softening up program.....working on a new Brittany puppy.....if that doesn't soften you up, nothing will.... 
