The most powerful city in the world awoke to find itself an Alpine village yesterday, covered by a 17-inch blanket of snow that reminded Washington's meek as well as its mighty that Mother Nature cannot be regulated.

It was a good excuse to spend the day in bed, in front of the television or by the fireplace. Many apparently did just that. But those who ventured out of doors found that Friday's blinding, blizzard-like conditions had been replaced by brilliant sunshine.

For those with nothing more important to do, the seat of federal government became a winter resort, its streets a place for skis, snowmobiles and dog sleds.

Even President Reagan and the First Lady were stuck at home. Had they looked out to the south yesterday, they would have seen more than 1,000 people in sweaters, parkas and wool caps circling the Ellipse on cross country skis in the Winter Festival being held there.

Hundreds, among them Randy Teach, a U.S. Health and Human Services employe who walked from his apartment in Southwest, waited in line for about 30 minutes before donning boots and skis provided free for the third-annual event.

"It's the only thing going," said Teach. The storm, said one organizer, was "a wonderful coincidence." Snow machines, looking like giant spiders trapped in the drifts, stood idle.

Many found the storm reason enough to celebrate. On Apple Cross Terrace in Damascus in the Maryland suburbs, families helped shovel out one another's driveway, then set up a charcoal grill in the middle of the street and held a block party over hamburgers and hot dogs.

"It's a once-in-a-lifetime thing," said accountant Mike Kelly. "Everyone's in a good mood. Usually in winter they're all shut in their houses. This brought them all outside."

Indeed, the sense of community that errupted with the Redskin's Super Bowl victory seemed rekindled by the storm. Neighbors banded together to make streets passable. Near Macomb Street NW, residents removed a manhole cover and pushed the snow directly into the city's sewers. The neighbors then repaired with sleds, toboggans and garbage can lids to the slopes at the nearby Washington International School.

For most of the day, downtown Washington was a pedestrian's paradise. Pennsylvania Avenue in front of the White House was a six-lane deck of white. Side streets were playgrounds.

Still, some motorists were determined to bring things back to normal. Jack Machey, an engineer for National Highway Traffic Safety Administration who customarily plows snow for neighbors in Fairfax Station, found his four-wheel-drive pickup no match for the accumulation in his driveway.

"I got stuck twice already," he said at noon.

For some, the storm will have lifelong associations. At least two hospitals in Northern Virginia reported something of a baby boomlet. Arlington Hospital reported nine women got through the snow to have their babies there and at Fairfax Hospital a head nurse said she was "too busy to count." All the hospital's delivery rooms were in constant use through the night, she said.

In Prince George's County, another baby was trying to be born, but the mother was snowbound at home in Laurel.

"I'm having a little bit of pain," said Maria Lugo in a telephone interview. "I think it's coming any minute now."

At 4 p.m., police said Briarchip Street to the Lugo's house was blocked off from Rte. 197. Authorities were waiting for a snowplow they had dispatched so that Lugo could be driven to Georgetown University Hospital.

"It's our first one and we're really excited about it," said the expectant father, Jose Lugo. "I just knew that baby would come in the storm."

In West Springfield, residents speculated on when the snowplows might arrive to free them. Couples walked arm-in-arm down the middle of Carrliegh Parkway, stopping to exchange greetings with neighbors.

David Johnston, an architect, used a garden hose to tow his young daughter up a hill where children had constructed a ski run. Johnston quit after two trips, remarking that that "the tow wears out faster than the skier."

Cornelius Cokley became instantly popular among his North Arlington neighbors after coming home yesterday with a front-end-loading tractor he rented through his Merrifield construction firm.

A few blocks away, Jimmy Pickett was chipping away at a wall of snow a plow had left next to his car. "I'm not worried about shoveling," explained Pickett. "When I get this car out of here, I'm going right back to the guy who sold it to me and leave it there till he fixes it."

Lin Murphy and Sallie Greenwood left their car in the snow to ski down Williamsburg Boulevard in Arlington. "Why fight nature?" said Murphy, an Internal Revenue Service lawyer who said she used to ski to work daily when she lived in Saskatchewan. "Why not just go along with it?"

There were intimate scenes at many restaurants and hotels, where many travelers had been stranded overnight, some unable to find rooms. Willie Galloway, manager of a Grand Union supermarket just outside Alexandria, had been unable to return to his home in Upper Marlboro and spent the night at the store and was planning to stay the day yesterday earning overtime stocking shelves.