I've used a cold steel trail hawk in the woods to cut firewood and it worked, but the handle was to short to suit me. I think the handle on mine is 19". Am guessing that 24" would work better for me. Because of this, I went back to carrying a Khukri or Machete instead of a hawk.
This spring I when I'm backpacking I plan on carrying a Machete or Khukri, small Axe and a saw. That combo Should handle anything from brush, to branches to big logs acrost the trail. Have not desided which machete yet, though I'm leaning towards something in the 14 to 18" range. The Axe will be a 1.75lb to 2.5lb hudson bay style and the saw will be a 30" or 36" bow saw.
By the way, Great River Forge makes a French style hawk with a 16oz head. I have one that needs a new handle (to many throws and misses) and am planning to make a 24" handle for it. That thing is awesome! It came from GRF with an 18" handle and when I did a side by side with my trail hawk, in my hands it out chopped it. My favorite hawk. Would love to have him make me an axe head with the same shape as the French hawk, but one that weighs between 28 and 32oz.