VENICE, JUNE 4 -- Either because of or in spite of a special king-size bed flown in to accommodate President and Mrs. Reagan, the first lady did not sleep well Wednesday night after their eight-hour flight from Washington.

Elaine Crispen, Mrs. Reagan's press secretary, said the president slept just fine (from 1:30 to 9 a.m., according to his spokesman), "but Mrs. Reagan never does."

But the bed in question, flown from Portugal to the 17th-century villa outside Venice for the first couple to sleep on until the economic summit starts Monday, won't be moving with them to the Hotel Cipriani.

Reagan's spokesman, Marlin Fitzwater, said today that the revelation of plans to transport the bed from Portugal to Italy had caught Nancy Reagan by surprise. And the first lady made it clear that the bed was not to be moved when she and the president change hotels on Monday.

"She wasn't aware it was going there (to Villa Condulmer) and she didn't want any special accommodations," said Fitzwater of presidential assistant William Henkel's decision to take the bed out of storage in Portugal and fly it here.

Today the Reagans went for a 15-minute walk around the villa grounds, site of a former monastery. According to Fitzwater, before they were rained out, they observed several rose gardens and a pond taken over by wild ducks. They ate lunch on a canopied terrace watching the rain.

The Reagans have abandoned their once-favorite jet lag diet involving an elaborate program of feast-and-famine eating. Today they each simply ate a salad for lunch. Crispen said she suggested that Mrs. Reagan try eating some pasta for dinner tonight because it has been her own experience that she often falls asleep faster after indulging in such a meal.

"Mrs. Reagan said she'd consider it," Crispen said.

If pasta doesn't help, maybe a movie will. The Reagans brought with them the videotape of a colorized John Wayne film, "Angel and the Badman," starring Gail Russell and Harry Carey.

"The Reagans aren't going to watch it alone," Crispen said. "They've also invited the staff staying at the villa to join them."

Not all the welcomes awaiting the Reagans were friendly, despite ABC White House correspondent Sam Donaldson's shouted Italian greeting of "Buona sera, bella, bella" to the first lady upon arrival here last night and several bouquets of flowers sent to their room by Italian friends.

Outside the villa, located about 11 miles from Venice, protesters from Italy's Radical Party, led by two members of parliament, gathered to hoist a banner that proclaimed:

"Welcome President Reagan in a country where there is no death penalty."

The demonstrators also carried a petition, purportedly bearing half a million signatures, that implored Reagan to commute the death sentence of Paula Cooper of Indianapolis, who was found guilty of murdering an elderly teacher at the age of 15.

"We are asking, as the European Parliament did on 14th May 1987, for a change of the death penalty, inflicted to Paula and to all young people under age waiting to be executed, into a sentence of imprisonment," said an English-language statement released by the party.

The Reagan staff is billeted at several hotels in the area, including the Ogo Doglio outside Venice. ("I call it the imbroglio," said Fitzwater, without elaborating on the reasons.)

In their rooms, guests in the presidential party found brochures describing special hotel facilities, including a mud bath. Life styles are so relaxed there, according to the brochure, that guests are urged to come downstairs for breakfast in their bathrobes before moving on to the mud baths.

Both Crispen and Fitzwater demurred. The first lady's spokeswoman wondered if the mud was clean. As for Fitzwater, he remarked: "I'm not a robe man myself. And I'm definitely not into mud."