Guysssss I can't find oak wood T~T help please. I'm trying to do the "little chores" thingy for Logan
To add to what Welp stated, go to the forest (ideally during the day) and keep exploring while you have a hatchet in hand. You'll eventually find a somewhat special event which will let you chop for wood.
I will also reemphasize that it does take awhile to run into it, but red berries are always useful, so hey.