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if you have to make a shelter every night and use a fire for warmth and cooking, i would go hatchet or 3/4 axe. if this is more of a stationary camp, i would go full axe.
if you have a tent and sleeping gear and a stove for cooking, then i would bring a mid size fixed blade (my mora). it will be mostly for food prep and splitting up small pieces of wood for occasional "feel good" fires, so it doesn't need to chop and it should be light for going longer distances...