The first lingering cold wave of the winter of '81 hung over Washington yesterday, bringing bone-chilling winds and biting temperatures to this almost Southern town, and leaving patches of ice and snow clinging tenaciously to side streets and porch steps.

But John Miles was up and out of bed at 7, accompanying children from the Edgewood Terrace neighborhood in Northeast Washington on a sightseeing tour of the city, one last summer-like fling before the city goes into hibernation for what weathermen predict will be a bitterly cold winter.

The blue, double-decker "Spirit of '76," tourbus careened through the streets past the Capitol, where snow covered the riggings for Ronald Reagan's inauguration later this month, past the reflecting glass domes of the Botanical Gardens and the marbled front of the Supreme Court.

There was a tour of the Jefferson Memorial and visits to the grave of the late President John F. Kennedy and the changing of the guard at the Tomb of the Unknown Soldier.

"It was cold," said one of the 40 youngsters who made the trip. "But it was fun."

By mid-afternoon, a determined sun had brought the temperature up to 39, its high for the day, salvaging what might have made outdoor activity unbearable bitter.

Within no time, joggers were out -- some in shorts, steaming like out of season crabs as they cut through the cool, clean air.

Children were content to make snowballs from the patches of gray slush and ice that remained and hurl them at their friends, or chase each other down hills. Occasionally an almost-new Christmas wagon or bicycle could be seen, but those sights were rare.

Meanwhile, colder temperatures were forecast for the area today. "We won't see 20 degrees," said Ken Shaver, a meteorologist with the National Weather Service at the Baltimore-Washington International Airport.

The low Sunday night is expected to range between 5 and 12 degrees, with a 10 percent chance of a fresh supply of snow on Monday, according to weather forercasts. Bitter cold was predicted for the Chesapeake region, while a snow emergency declared Friday remained in effect for western Maryland.

In some outlying areas where conditions are decidedly cold but not dangerous, this kind of weather means fun -- skiing, ice skating, ice fishing, and hunting.

In the section of Edgewood Terrace where John Miles lives -- he calls it "poor, but not the poorest" -- the wintertime fun is dampened by the high cost of heating oil and food.

But yesterday, there was just enough sunshine to stave off the wintry withdrawals for a while longer -- at least for himself and a few more kids.

"I guess this trip culminates the outdoor activities that we've been involved in since spring," Miles said of the children's last excursion. "It can get awful cold around, so we'll stay indoors and read, play games or study for the SAT tests. But you can't beat getting out and seeing what's going on around you."