Roger, thanks for the info on hardness. Makes sense.
I was pondering the whole axe question and while I'm with Buck - an axe just doesn't go backpacking with me, for those were so inclined:
Saws are lighter and far more efficient to crosscut a branch, small (dead!) tree trunk, or log. So the purpose of the axe, in my mind, is to split those rounds into kindling, to get to dry wood inside a round, or to make small pieces for your wood-burning stove.
You could avoid needing head weight and handle length if you bring a wedge instead of an axe. Whack the wedge with a rock or a 2-3" diameter stick to split the rounds into firewood.
An old axe head makes a cheap wedge if you want to try the concept, although not UL.
An old axe head, with the eye cut off and the reminder cut in two, could make two small cheap wedges. As could bar stock in any number of alloys. There are times you want two wedges - like when you get the first one stuck (usually because you tried to split something with a knot in it). Any chainsaw shop sells plastic wedges to hold open a cut (but be safer around a chainsaw blade). In a pinch, I've used those to free a splitting wedge. Cheap ($6?) and light.
By cutting short rounds with a saw, you could not be asking so much of the axe and could use a wedge and (found) hammer to split it up.