As of 2009, less than a quarter of a percent of the land base in Alaska was "private land" ownership [see reference 1], adding up to approximately .9 million acres in Alaska. Government entities including federal, state, and municipal lands made up almost 88% of the land area or 320 million acres. Of that total, the federal government controls 69%, leaving the state with approximately 98 million acres (or just over 30%). Alaskan Native lands comprise approximately 44 million acres, which is a bit more than 12% of the total land base (which is overseen by regional and village Native corporations).
With most of the land being owned by public entities or tribes, you will most likely need a permit if you want to go off your property to cut firewood. The Alaska Department of Natural Resources Division of Forestry (DNR), the Bureau of Land Management (BLM) and the US Forest Service (USFS) offer firewood and personal use timber cutting permits. Regarding state lands, contact your local Division of Forestry office for more information.
Contact the local Bureau of Land Management office and the USFS office Tongass National Forest or Chugach National Forest for more information on firewood and personal use timber programs, on those lands.
Keep in mind that twelve of the 13 Alaska Native Regional Corporations do own private land, and some corporations allow firewood cutting by anyone who pays a fee and obtains a permit while others only allow access to share-holders.
1. “Who owns Alaska?.” Resource Review pg.1 2009 Alaska Resource Development Council