Honestly, I carry a small "hand axe" in the winter a lot, as I go where I can make fires. I am weight conscious in the winter but not ultralight. I am more or less dead set against "hatchets" - they are too small to be useful. Somthing akin to the small granfors forest axe is good, (I have one) and the cheaper and just about as good alternative is the smaller size fiskars axe. (with the 19 inch handle).

I'm not really convinced about the "combination" thing - looks too gimpy to be good at either, and "small" axes and saws really are at the edge of usefulness.

when on a sled I take the small axe and a medium size bow saw with a good blade.

Now, having said that, outside of deepest hardcore winter - this is a lightweight backpacking forum! I don't carry an axe normally (I break wood with my hands) and I certainly don't carry a hammer. (I've been known to pick up a rock or a log to bash in my tent stakes).