London (CNN) -- Lisa Suarez's voice breaks as she stands in the snow outside London's Heathrow airport, unable to get a flight home to Dallas, Texas.
"It's very hard," she says. "All I want for Christmas is to hug my daughter."
She and her family are among hundreds of thousands of people stranded by "freak weather conditions" that dumped unexpected tons of snow on Europe this weekend, snarling flight schedules at the continent's busiest airports.
Heathrow planned to cancel all arrivals Sunday, but later said it might allow three planes to land. A dozen long-haul flights are scheduled to take off Sunday night, spokesman Andrew Teacher said. He did not say which ones.
Charles de Gaulle airport in Paris told travelers to expect two-hour delays and cancellation of a quarter of flights. One in five flights was being canceled at the French capital's second airport, Paris-Orly, with delays of an hour expected, Aeroports de Paris said on its website.
Germany's Frankfurt airport said at least 500 of a planned 1,300 flights would be scrapped Sunday.
And more snow is expected in Germany during the day, which will put further strain on flight schedules, spokesman Waltraud Riehemann said.
More than 200,000 passengers were due to take off from Heathrow on Sunday, said Donna O'Brien, a spokeswoman for Heathrow airport operator BAA. Most won't be able to, she said.
Workers were trying to remove 30 metric tons of snow from each of the airport's 200 aircraft parking stands, according to the airport's website.
Meanwhile, ground travel in France was also snarled by heavy snowfall and cold temperatures. The U.K.'s Foreign and Commonwealth Office said Sunday that French authorities reported they are preventing all cargo trucks and buses from using roads in northern france and the greater Paris metropolitan area, and that car travel is "unadvisable." Air and rail services were also affected, the office said.
The adverse weather in France even affected pop singer Lady Gaga, who said on her Facebook page that all 28 of her tour trucks had been detained by the government for more than 24 hours.
The Lady Gaga concert set for Sunday night was rescheduled for Tuesday, according to the website of the Palais Omnisports de Paris-Bercy, where it was to be held. A Monday concert remains scheduled.
Paris police said that since noon Saturday, more than 1,300 trucks had been barred from entering Paris, and no trucks were being allowed to circulate in the city. They could not confirm whether Lady Gaga's trucks were among them.
In other travel news:
--Britain's Automobile Association helped more than 3,000 drivers by 10:30 Sunday morning, and was getting 800 calls for assistance every hour, it said. It expected 14,000 call-outs by the end of the day, nearly twice the average on a Sunday. Another organization, the RAC, said it was getting 1,500 calls an hour to help drivers, mostly in Scotland.
--London's Gatwick airport says its runway is open and "operations are gradually returning to normal."
--Heathrow will have no flights from Terminals 1 or 4, and only a small number from Terminals 3 and 5, it says. Terminal 2 is closed for renovation.
--Heathrow urges passengers to check with airlines before flying. Contact numbers are listed on its website, www.heathrowairport.com
--British Airways tells passengers to check www.ba2go.com before coming to the airport. Customers who need to rebook in the U.S. should call 1-800-247-9297. Those in the UK should call 0800 727 800. BA warns of high call volume despite hiring extra call center staff and urges people to call only if necessary.
--BMI cancels all flights to and from Heathrow and asks passengers not to come to the airport.
--British train operator Network Rail says trains are running more or less normally, but advises passengers to check before traveling.
Heathrow is Europe's busiest airport -- and one of the busiest in the world. Paris Charles de Gaulle is second, and Frankfurt sees the third-highest traffic on the continent.
Forecasters say the United Kingdom will remain in the grip of bitter winter weather at least through Monday.
Heathrow employees are working to try to make the airport fully operational by Monday.
"We've got a few thousand people that have, unfortunately, had to spend the night," BAA spokesman Teacher said Sunday. "We've been making them as comfortable as possible with blankets, with food and water."
Teacher said ice is the main problem affecting flights.
"We are extremely sorry for the disruption that's been caused to people's journeys today, but the decision has been made simply to avoid any kind of potential risk," Teacher said.
"These are absolutely ... freak weather conditions," he added. "We've not seen a storm like this in 20 years."
On Saturday, frigid temperatures and extreme conditions pummeled Europe. From Northern Ireland to Bulgaria, blizzard conditions left airports with heavy delays or shut them entirely. Snow, ice and fog have caused travel chaos ahead of a busy holiday travel week.
And severe weather could continue on Monday as another series of weather systems move in, said Met Office special forecaster Tony Burgess.
"There is another risk of [heavy snow] across England and south Wales on Monday," Burgess said.
The next wave of snowy weather is expected to bring up to 20 centimeters (8 inches) to some parts of the United Kingdom, with London expected to receive 5 to 10 centimeters (2 to 4 inches) of snow.
The weather system will move across France and Germany on Sunday. Below-normal temperatures are expected to continue in northern Europe into the beginning of next week.
Journalist Nina Dos Santos and CNN's Frederik Pleitgen, Katy Byron, Kathryn Tancos, Mila Sanina, Boriana Milanova, Hada Messia, Per Nyberg, Peter Taggert, Denise Quan and Charley Keyes contributed to this report.