On the new videos, the guy moving the lumber says, "Here for work? Grab an ax, and cut all the wood you can hold."
Maybe this means we can cut trees down? Discuss.
That is not what he said. He says: "Here for work? Get an ax. Bring me all the wood you can chop."
I see this playing out a few different ways:
1.) There will be a designated area you find with the quest arrow where you can "chop wood". This could be as simple as striking a specially designed tree which has a pre determined cut off area at the base and then after it takes so much damage it falls over and then you can either put it in your inventory, or use the Z button to drag it along like you can drag bodies in fallout new vegas. It's much better than Oblivion, once you press Z on a dead body it's being carried and you don't have to HOLD it down. So you drag stuff around and then press Z again and it drops. I can see this being the most realistic way to transport chopped wood.
2.) There is a specific pile of "logs" which you chop and wood is added to your inventory with each strike, until you can't carry any more. Then you sell him the wood you chopped.
3.) The dead logs that you find laying about in the environment at various places, perhaps you hit them with an axe and it breaks down into smaller pieces which you can put in your inventory and sell to him. This would limit how much you can make. Or maybe he just said grab an ax for immersion, but all you really do is simply find wood in old logs like harvesting any plant.
There are other ways it could be done obviously, but who knows maybe any tree can be chopped down. They are just nifs, all they would need is a simple script. It's not like the player would make time to cut down every tree, lol. I think it would be pretty cool dragging trees around with the Z key rather than have wood in your inventory, so hopefully its something like method 1.