(CNN) -- The mid-Atlantic region continued digging out Monday from the weekend's record blizzard, but snow-weary residents learned of a new winter storm due in the area on Tuesday.

The National Weather Service issued a winter storm warning, with predictions of another 10 to 20 inches of snow, for northern Virginia and eastern Maryland, including the District of Columbia, beginning Tuesday afternoon and continuing through Wednesday.

"A winter storm warning means significant amounts of snow are expected or occurring," said the statement from the weather service facility in Sterling, Virginia. "The combination of snow and strong winds will make travel very hazardous."

If as severe as predicted, the new storm would be the third major snowfall to hit the nation's capital and surrounding region in just over seven weeks.

In last weekend's blizzard, a record 32.4 inches of snow fell on Washington's Dulles International Airport over two days, breaking a January 7-8, 1996, record of 23.2 inches.

Federal workers in Washington, with the exception of emergency employees, stayed home Monday and students in most schools in the nation's capital got a snow day.

Many residents who spent the weekend playfully making snowmen and hurling snowballs also grumbled as they shoveled hip-high snow from driveways.

"The streets are pretty well covered," Kingsley Barreto said Sunday about his subdivision in Gaithersburg, Maryland.

"No cars coming in or out of here. Hopefully everyone in the community has enough supplies to last them for a little while, because it doesn't look like we're going anywhere anytime soon," Barreto said in a post he submitted to iReport, a CNN Web site that allows people to submit information, pictures and videos.

Watch Barreto's iReport on his neighborhood

Crews worked around the clock to clear roads and repair power lines, warning that it might take days to restore electricity to some customers from Pennsylvania to Virginia.

Two of Dulles' four runways were open Monday morning, and officials hoped to have a third open later in the day, said Courtney Mickalonis of the Metropolitan Washington Airports Authority.

The situation there is "getting back to normal," Mickalonis said.

But airport officials asked travelers not to go there without confirmed flights.

Reagan National Airport was scheduled to reopen at 10 a.m. Monday, with flights resuming on a limited basis, the airport authority said. Travelers were urged to check with airlines on flight schedules before heading to the airport.

Baltimore/Washington International Thurgood Marshall Airport was open Monday, with limited service, spokesman Jonathan Dean said.

One of the two runways opened Sunday night, and some flights landed, Dean said. However, airport authorities expect carrier delays and cancellations because of the backlog.

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Airport crews were dealing with a refreeze from overnight, but officials intended to have both runways open by the end of Monday.

Amtrak canceled several trains Sunday after trees and power lines fell on tracks, the train service said. Dozens of Greyhound bus trips in mid-Atlantic states also were canceled, the company said on its Web site. And officials across the region advised drivers to stay off slick roads.

"Everybody's just trying to clean up and get a little bit ahead of the game before the next round comes," said Michelle Timberlake, who lives on a farm in Boyce, Virginia, about two hours west of Washington.

The interior designer found herself running through a mountain of snow when about 40 cows escaped from the pasture on her husband's farm in search of food and shelter.

"This was not what I imagined for myself," she said Sunday, laughing about the experience.

CNN's Sarah Lee, Sarah Aarthun, Justin Lear and Rachel Rodriguez contributed to this report.