The USDA Forest service may have firewood permits.
Pacific Northwest Region
Forest Service
333 SW First Avenue
Portland, Oregon
Also might try the U.S. Government Bureau of Land Management (BLM).
Oregon State Office
Bureau of Land Management
333 S.W. 1st. Avenue
Portland, OR 97204
503-808-6002
You'll want to go to the the Mt. Hood National Forest. or across the river to the Gifford Pinchot National Forest if you choose that option. Now is the time to get firewood for next winter, not this winter, unless you luck out and get a recently felled snag.
The best time to get firewood off the National Forest is in the winter, after a windstorm. On the Gifford Pinchot, called the GP, you can get a firewood permit, and take what is in the road. In some places, you can go beyond the road edges. The other good time is to follow the snowline in the spring, and get the trees that are across the roads.
I am not familiar with the policies of the Hood. They have offices in Sandy, Estacada, and that place over in the wheatfields that I can't remember the name of right now. The GP has offices in Vancouver, Trout Lake, Amboy, and Randle.
The office in Portland is in the Federal Building downtown. It is the regional office for Washington and Oregon offices and is like entering a fortress..metal detectors, security guards, etc, so call there first.