The US Forest Service roads on National Forests are federally owned. They all are numbered in theory, but you can't always find them marked. State owned lands are managed by the WA State Dept of Natural Resources (DNR). Not sure where you are getting this idea about all the state land being leased to tree farms.
Timber sales take place on Nat Forest lands. Private logging companies bid for stumpage (forest trees on the stump). They are responsible for building and improving roads on Nat Forests which get numbers and become part of the USFS road system.
There is rarely logging in parks. This fall I saw the unbelievable loaded log trucks driving across Yosemite NP.
