Back in the old country it was pretty common to have a fire on a backpack in the woods. In fact in winter we'd often carry a rectangular canvas tarp and use it as a heat screen (strectched at 45 derees) on a side of a special type of fire (see below) that burned all night. No other shelter in below zero temps.
I don't like fire anymore. Too much impact.
In order to get firewood a group would normally carry an axe and a saw. A crosscut saw (or lumberjack saw):
http://en.wikipedia.org/wiki/Crosscut_saw
I used to carry the saw on the side of my pack under the compression straps. We'd find a standing dead tree, cut it and get fire going.
Same goes for winter mountaineering trips where we'd normally carry a large floorless pyramid tent and a metal wood stove. Be above the tree line during the day, drop down for the night. This called for smaller trees.
An axe would normally only be used to split logs. Yet, it is possible to use an axe to cut a large trunk effectively. You need an axe on a longer handle and with a very narrow blade.
Here in Boulder there's a mountaineering shop that in fact sells just such axes. Imported from Norway or Finland or some such.
In most cases though, if you have at least two people a crosscut saw will be orders of magnitude easier to use.
Again, I am not a fun of fires and do not even like them. Yet, hunters in taiga would use a fire to spend a night in winter.
What you want in firewood is a *DEAD STANDING* evergreen tree. Pine worked very well. Not sure about fir. An evergreen will be dry and have an accumulation of highly flammable sap near the top. You can easily get the fire going in the most wet and cold conditions.
If you need a fire to burn the whole night do this. Find the largest trunk you can move. Cut 3-4 pieces from the bottom 6 feet long. Place 2 logs side by side next to each other. Start a fire on the top of the 2 logs. Once the fire is going put the 3rd log lengthwise on top. Have another 6 feet log ready to put on top after 6 hours or so. You can sleep along the side of the fire. This (I believe) is used by Siberian hunters. My friends and I have spent many nights by this type of fire.