The government will give Wolf Trap Farm Park half the funds needed to rebuild the Filene Center and loan the park the rest, according to a plan announced yesterday by federal officials. The center was destroyed by fire April 4.

However, Rep. Sidney Yates (D-Ill.), whose subcommittee must approve the proposal, questioned yesterday whether the officials had enough information yet and called their press conference "premature."

The press conference was called by National Endowment for the Arts chairman Frank Hodsoll and held at the NEA offices. Also present were Interior Deputy Assistant Secretary for Administration Richard Hite, Wolf Trap Foundation board president Carol Harford, Sen. John Warner (R-Va.), and Rep. Frank Wolf (R-Va.). Hodsoll and Interior Secretary James Watt were designated by President Reagan the day after the fire to form a task force to assess the damage and evaluate the federal government's financial obligation to Wolf Trap. The park is maintained by the National Park Service, and the center was uninsured.

The 50-percent loan will have to be repaid from private donations "promptly," Hodsoll said. Wolf Trap founder Catherine Filene Shouse had urged the government to pay 80 percent of the rebuilding cost, leaving 20 percent to be paid by private contributions.

"I certainly want to congratulate the executive branch for its 'can do' spirit," said Sen. Warner. "I'm cautiously optimistic that it will be approved in Congress. While 80-20 federal/private contribution to rebuilding would have been preferable, 50-50 is fair and the best way to get approval from Congress."

The federal government has produced neither final design proposals for the new theater nor a final estimated cost for rebuilding. Tentative estimates fall between $17.5 million and $20.3 million, according to Wolf Trap officials.

But Yates was puzzled by yesterday's announcement. "I don't understand what the purpose of the press conference was," said Yates, chairman of the House appropriations subcommittee on the interior. "As far as I know, they don't have approval of OMB Office of Management and Budget . From the information I have, there is no new information . . . They have a range of figures with no official approval. They have no report from the task force . They don't know what the cost will be . . . What are they going to build? The same kind of structure? They better find out how much it will cost, what they will do, and get the administration's approval before they come to Congress."

However, Hodsoll said, "We have the approval of the president. I was basically asked to do the press conference by the White House." Last week Hodsoll and Watt gave the White House a report "as to where we were," said Hodsoll. Based on that, the president made a decision about the general plan for supporting Wolf Trap and personally called Shouse last weekend, Hodsoll said.

"We still have a report to put together on costs and potential design alternatives," Hodsoll said. "We're going to have to have a number, no question. But we have to go ahead to find out if the general format is okay to members of Congress .

Although the proposal falls short of what Wolf Trap wanted, Shouse, who is recuperating from a hip injury at her Virginia home, issued a statement calling the White House decision "a vote of confidence in Wolf Trap as a national institution" and "a heartening response to the outpouring of public concern." But she called for the public to help do its part. "We still have a long way to go . . . We will need approximately $10 million from the community as its share of the rebuilding effort."

Wolf Trap and NEA officials expressed optimism that the park can raise that much. Wolf Trap has raised $943,169 so far, according to Shouse's statement.

Any federal loan, Hodsoll said, "will have to be repaid promptly. It's a device to get the building going quickly." The terms of a loan have not been set yet.

Wolf Trap is convinced it can rebuild in less than a year. The goal is to be ready in June 1983, for the summer season, Harford said.

However, the Interior's Hite said at the press conference, "I don't want to appear pessimistic, but spring of 1983 is awfully optimistic for building a structure like the Filene Center. We have plans to complete. We have a package to negotiate with Congress. I wouldn't put money on the spring of 1983."

Wolf Trap's government relations consultant, Robert Mendelsohn, countered later: "When Hite says he wouldn't bet on 1983, he's thinking about normal construction time for the government. I guarantee that in the private sector you can build a building like the Filene Center in nine months."

National Park Service investigators have not yet found the cause of the fire, according to Hite. "The only definitive thing I can say is that there has been no evidence of arson," he said.