Heated by their causes, if not the 10-degree temperatures, several hundred anti-Reagan demonstrators marched up Pennsylvania Avenue yesterday in a counterinaugural parade to protest unemployment, U.S. involvement in Central America, South African apartheid and a host of other issues.

The protesters, ignoring the weather-forced cancellation of the official presidential inaugural parade, rallied near the U.S. Capitol during Reagan's noontime swearing-in, then trooped to Western Plaza a block from the White House and laid claim to a section of bleacher seats that had been intended for inaugural celebrants.

"He may have canceled his phony-baloney parade," said Larry Holmes, a 32-year-old organizer with the People's Anti-War Mobilization. "But he didn't cancel unemployment, he didn't cancel the budget cuts, he didn't cancel the war in Nicaragua, he didn't cancel support for apartheid."

Later, at the South African Embassy, another group of demonstrators began the 10th week of apartheid protests there, which resulted in 19 arrests yesterday.

At Western Plaza, 14th Street and Pennsylvania Avenue NW, demonstrators, some of whom came by bus from New York, Texas, Minnesota, Michigan and California, shivered in a biting wind that whipped their banners. Tiny icicles hung off beards and moustaches.

But the marchers, a few of them in wheelchairs or on crutches, seemed buoyed by their ability to pull off a protest in the frigid weather that had scared off the president and inaugural parade planners.

"Once Reagan canceled, we sort of took it as a challenge," said Holmes, who lives in New York City.

The cold weather did take its toll, though. Protest organizers had predicted up to 5,000 participants. Police estimated only 200, though the actual count looked closer to 500.

Undaunted by either the weather or the hostile stares of Reagan supporters -- some of whom rode by in limousines or watched from hotel rooms overlooking the avenue -- the protesters talked of being "fired up" by anger against Reagan's policies at home and abroad.

"While they are having their parties, there's a whole other America on the outside," said Michael Kramer, a New York City government worker and a member of the All-Peoples Congress, one of the protest groups involved in organizing the demonstration.

"We've come down here to see that the right thing is done," said Emma Curry, who described herself as a 53-year-old housewife from Detroit. "We just want to see justice done."

Some onlookers, however, were less than pleased by the sight of the demonstrators.

"They're liberals," said Basyle Tchividjian, a Fort Lauderdale, Fla., teen-ager who said he was invited to the inauguration by his grandfather, the Rev. Billy Graham. "They're communists, I think," he added, hurriedly snapping photographs of the marchers.

The protest lasted about two hours, featured chants, songs and speeches and concluded with anothmarch to the Harrington Hotel, 11th and E streets NW, where demonstrators were served hot soup.

D.C. police reported the arrest of one protester, Kenneth S. Toglia, who was accused of spraying the words "No War" on a wall of the FBI Building and was charged with defacing government property.

At the South African Embassy, the Rev. Joan Campbell, assistant general secretary of the National Council of Churches, and Bishop Alfred Dunston Jr., of the African Methodist Episcopal Church in Philadelphia, were among 19 persons arrested in demonstrations against apartheid.

Campbell said the cold she and about 50 demonstrators felt yesterday was "nothing in comparison" to the years of pain endured by blacks in white-minority-ruled South Africa.

Randall Robinson, coordinator of the ongoing antiapartheid protests, said 813 people have been arrested in 11 cities since the demonstrations began at the embassy Nov. 21.

Robinson said that protestors have forced the resignation of two Americans who served as "honorary consuls" for South Africa in Boston and Portland and persuaded three banks in Pittsburgh, Minneapolis and Miami to stop selling Krugerrands, the South African gold coin.