>>10003079If you get a folding saw (like a folding knife) don't cut using the full length of the blade. Tension and torque will snap the tip very easily, only cut using the middle part of the saw. A pocket saw will only cut small piece of wood and a hatchet can also do a similar job. A collapse saw (pic related) will let you take about 10 inch diameter wood.
Something else to consider is a pocket sized multi-sharpening tool. Assuming you'll be innawoods for more than a few days. Get one that will let you not only sharpen knife and hatchets but also the saw teeth. When you first get the cutting tools you should sharpen them then rub them down with knife oil. This will prevent them from rusting when in storage.