The Carter Administration is proposing to eliminate virtually all federal support for the performing arts in the nation's parks, including $1.2 million in funds for Wolf Trap, Ford's Theater, Carter Baron and the Shakespeare Summer Festival at the Sylan Theater.

The cuts, contained in the fine print of the budget President Carter submitted to Congress earlier this week, will end the 18-year-old Shakespeare festival and possibly force Ford's Theater to close down -- if Congress sustains the cuts.

The impact will be felt almost exclusively in the Washington area since the National Park Service has only one other national park with a professional theater, at Chamizal National Memorial in E1 Paso, Tex. No budget cut is proposed for Chamizal.

The cuts would end $175,000 in annual grants the Park Service has given Ford's since 1971, when the theater was threatened with bankruptcy.A $23,000 yearly allotment for stagehands would also go.

"I don't see how Ford's can survive... without Raising prices beyond what people here are willing to pay," said Frankie Hewitt, executive producer of the historic theater where Lincoln was assassinated.

Hewitt, who helped convince the Park Service in 1968 to make Ford's a working theater and not just a museum, said: "Frankly, I don't know what's going to happen... we're having enough money problems as it is... we might as well just turn it back to the Park Service and let them handle it. It's all very depressing."

Ford's operates on a $1.75 million budget, 90 percent of it from ticket sales and donations, Hewitt said.

Wolf Trap stands to lose $857,000, or the lion's share of the $1.2 million, according to Park Service officials. However, the amount is in question as is the government's right to end support for Wolf Trap, says Carol Harford, president of the Wolf Trap Foundation.

Harford, who learned of the proposed administration cuts from a reporter, said "this catches me absolutely by storm... nobody's said anything to us about it... but we have a cooperative agreement with the Park Service to support" the popular outdoor theater in Vienna.

While the Park Service will continue to maintain all of the parks as parks, it is proposing to end support for stagehands at Wolf Trap ($450,000 this year and a projected $592,000 for fiscal 1980) and also end a general grant which this year is $150,000 and was projected by the Park Service to be $265,000 next year. The cuts at Wolf Trap and the other Park theaters are proposed by the White House Office of Management and Budget, not the Department of Interior and its Park Service.

Harford insists both the annual $150,000 and the money for stagehands are stipulated in the agreements and amendments the Park Service has singed since Wolf Trap was created in 1966 through donations of land and $2 million to build a theater from Mrs. Jouett Shouse.

"We hope Congress will assume its responsibility and pay serious attention to the philosophic impact of this... it's a national policy of support to the arts [the administration] is toying with," Harford said.

Wolf Trap's 1978 operating budget was $4.2 million, with $1.6 million of that in private donations and the rest in ticket sales, Harford said. She added that the Park Service money is considered technical support, not part of their operating budget.

The Park Service will spend $1.8 million at Wolf Trap this year, most of it to maintain the 100-acre park and its buildings. In fact, while it proposes to take money away with one hand next year, it proposes to give some back with the other, since the budget includes almost $500,000 to restore the Filene Center at Wolf Trap.

Federal support for the Shakespeare Summer Festival has been questioned for the past sevceral years, and the $150,000 for it has been knocked out of the budget and then replaced more than once.

This year, however, even the Park Service is questioning whether other types of summer theater programs might not be attemped, ones that cost little or nothing such as inviting amateur or university groups to use the Sylvan Theater beside the Washington Monument much as bands are invited from around the nation to play on the Ellipse to entertain visitors to the White House.

The cut at Carter Barron would end $33,000 used to provide free tickets to disavantaged youth. The Park Service no longer produces concerts or theatricals at the outdoor Rock Creek Park theater, but contracts with an outside producer and then buys blocks of tickets for kids.

The Kennedy Center, the premiere performing arts center on Park Service land, is not affected by the cuts since it has never used federal funds to support performances. Its $15 million budget is paid for with box office receipts and grants and gifts, according to Roger Stevens, chairman of the center's board of trustees.

The Park Service is spending $4.1 million this year and a proposed $4.3 million in fiscal 1980 to operate and maintain the Kennedy Center.

The White House is proposing to trim the Park Service budget nationally by about $3 million, to $383 million, which will mean a reduction in the Washington area of about 85 positions -- all to be made by attrition, according to Park Service officials -- and only a small budget increase to pay for built-in salary increases. However, $7 million in construction projects have been postponed here.