If i bring a shovel, i bring a good sharp swinging Axe. Not only for firewood at camp, but for clearing trees from trails. During spring runs i carry a chainsaw, but during summer, i leave it at home simply for fire danger, and who couldnt use a little axe workout.
for the terrain around here on the east coast, i want to start carrying a long handled bush axe. i fell in love with mine while surveying and cutting line in swamps and backwoods, i used it for everything from mowing tall grass to removing limbs and even chopping down small trees. its the perfect tool for clearing brush, so much safer than a machete or anything similar.
A good bow saw is easier to use for trimming wood to length; some folks seem to like to play lumberjack and cut wood so big that it really needs to be split with an ax to burn well (I find those trees too big to conveniently carry by hand; getting old, I guess).
...Been using an old, large size, folding Svensaw since the 1970's (pro'lly should get it sharpened; good for dead wood up to 6"-8" in diameter; about the biggest trees that I can drag to camp any more); never needed nor wanted an ax/hatchet in the woods... or anywhere else... but spring is approaching and some folks seem to like to use up excess energy, chopping...