You may only cut down trees on your land. We cant have you roaming around cutting everything down, its not a survival game you know.
You get wood from Trees
You get Hardwood from Tree stumps
If you leave the treestump in the ground a tree will regrow in its place in 1 - 2 months.
If you run out of trees you can plant your own on your land of course.
You can grow trees in all seasons, even winter.