There's a number of martial arts that use small axes. Combined with a shield or buckler they're pretty handy and can perform some surprise "reach around" attacks no sword could match. For combat the best ones have projecting points forward and back, to hook and jab. And the head should be thin in profile and light for slashing. The problem with most tomahawks is they're jacks-of-all-trade and have heavier heads for chopping wood. And of course there's a big difference between chopping wood with an axe and fighting with one. The swing is completely different, and you have to learn how to manipulate its axis of rotation. Not to mention basics such as "true time" fighting and biomechanics. Most of the big HEMA conventions will have a seminar on small axes.
But my favorite axe at this point is the two handed Great Dane from Arms and Armor. Light in the hand, well balanced and absolutely terrifying in drills. It's as fast in the hand as a longsword and can yank, spear, slice, push-cut or just simply bash. You can use it like a sword or like a pole-arm. But it would fall apart quickly if you tried to chop down a tree with it.
http://armor.com/pole024.html
But my favorite axe at this point is the two handed Great Dane from Arms and Armor. Light in the hand, well balanced and absolutely terrifying in drills. It's as fast in the hand as a longsword and can yank, spear, slice, push-cut or just simply bash. You can use it like a sword or like a pole-arm. But it would fall apart quickly if you tried to chop down a tree with it.
http://armor.com/pole024.html