Deep packed snow is not always readily available in the dense forest for igloo or snow cave building. While hunting in Siberian taiga (-10F - typically) we used to create 2-3 night open air camps in the woods, building personal or 2 people sleeping platforms around a huge campfire, surrounded by heat reflective and wind deflecting tarps. The platform consists of 2 parallel logs laid in radial (from the fire) direction, covered with smaller logs across them. Very comfortable and warm. Because the bed is elevated above the ground (about 20") it catches heat from the fire much more effectively from all sides. We had no well insulating sleeping pads back then. If you go to sleep on the snow, especially near the huge camp fire, your sleeping bag will be soaked with melting snow pretty quick.

Anyhow, that was just an example of a shelter building requiring a lot of wood cutting. If you travel with just a folding saw you can not build a huge fire, which could keep going unattended the entire night, anyway, and you would never even consider a possibility of building a serious long time shelter requiring more than a dozen cuts or so with that tiny saw.

After all, a wilderness BOB is not for pleasure hiking, it's for sustainable survival away from civilization. The only saw I can see suitable for that is this one:



But getting back to the templedog2 question: if I would face the choice of a single tool in his bug out situation, - it will be a long handle axe.