Is Timberline privately owned?

Yes, Timberline in most contexts is privately owned, though ownership depends on which Timberline you refer to, as there are several companies and resorts with that name. Timberline Lodge ski area on Mount Hood, Oregon, which is most famous Timberline resort, is privately operated by RLK and Company, owned by Richard Kohnstamm family, under a special use permit from US Forest Service, as the land is federal forest land but operations are private concession. The historic Timberline Lodge building itself is owned by US Forest Service but operated privately. Timberline Mountain Resort in Davis, West Virginia, formerly Timberline Four Seasons, is privately owned by Perfect North Slopes, which bought it in 2019, after previous private ownership. Timberline Building Products, which makes shingles, is part of GAF, which is privately owned by Standard Industries, owned by Heyman family. Timberline Construction companies are typically privately owned small to medium businesses. Sage Timberline software is owned by Sage Group, which is publicly traded, but Timberline as product name was acquired. Timberline Resources is publicly traded mining company. So most Timberline resorts and building products are privately owned or privately operated, not government owned, though they may operate on public land under permit. The Timberline Lodge is unique as public building with private operation, but overall Timberline entities are largely private.