THE United States paper and forest-products industry appears on the verge of a recovery, thanks to slowly growing demand and a reduction in planned future capacity."While the wood products industry will remain a cyclical one, we strongly believe that for the first time in 15 years the industry will enjoy substantial benefits from the coming improvement in wood product demand," notes a Prudential Securities analysis. But many of the people who work in the mills and factories remain skeptical. "We keep hearing about the end of the recession and the upturn in our industry, but we sure haven't seen it yet. Orders are very slow," says Curt Copenhagen, a spokesman for Longview Fibre Company in Longview, Wash., several hours' drive south of here. Longview Fibre shut down its pulp and paper operations for a week recently, sending many of its 2,000 local employees home. Nor was it the only Northwest company to do so. Weyerhaeuser Company announced it was going to briefly close a pulp mill in Everett, Wash., as well as extend a maintenance shutdown at a Canadian pulp mill for a few more days. Weyerhaeuser notes that demand for wood pulp is up slightly over last year, but price-cutting has meant thin profit margins for producers. The timber and forest-products industry has been hit especially hard in the Pacific Northwest in recent years, because of weak demand, the extensive exporting of logs - which has meant lower production in US pulp and paper mills. Thousands of jobs have disappeared, some because of automation. Plans to limit logging on millions of acres of federal forest lands to protect the northern spotted owl will mean another diminution in forest-related jobs. Press accounts continue to report unhappy stories about an industry that has been mired in deep trouble. Nonetheless, a growing number of experts maintain the industry is coming out of its doldrums. One new analysis, by IDS Advisory Group Inc., concludes that North America remains the world's "low-cost producer" of paper, lumber, and plywood. Thus North American paper and forest products will "increasingly gain market share" in world markets, says IDS, which is based in Minneapolis. Earnings should "accelerate rapidly" in 1992 and beyond for many paper and forest-product companies. Matthew Berler, a paper and forest-products analyst with Donaldson, Lufkin & Jenrette Inc., in New York, rates the industry as "favorable." Companies that make linerboard, uncoated freesheet, and wood products should particularly benefit from the modest recovery now under way in product prices and in demand. If the economy "were to grow at just 2.5 percent," instead of the more typical growth of 4 to 6 percent often experienced after the end of a recession, that should be enough to provide upward momentu m for forest-product companies, Mr. Berler says. Looking ahead, Berler says the 1992 to 1994 period should be good for many producers, including Georgia Pacific, Temple Inland Inc., Union Camp Corporation, and Willamette Industries. Moreover, companies that own their own timber lands, such as Weyerhaeuser, will be in a favorable position, given an expected reduction in logging on federal lands, he says. A number of positive factors warrant watching, says George Haloulakos, a senior investment analyst with the Seattle offices of Dain Bosworth Inc.: Paper prices have stopped falling, some order files are growing, and many capital projects that were planned by the companies have either been completed or put on hold. He says there will be a slightly smaller-than-expected increase in mill capacity during the next few years, which should benefit a number of companies. In the case of Longview Fibre, which is listed on the New York Stock Exchange, Mr. Haloulakos says that "back to school shopping and holiday buying activity during the next four months should boost the demand for both merchandise bag paper and linerboard. Low customer inventories imply that a nice uptick in demand should be immediately felt by papermakers."