Overnight snowfall has compounded transport misery for travellers in Europe, as it continues to struggle with freezing conditions.
Germany's main air hub, Frankfurt, was forced to cancel almost 300 flights after being hit by unexpected snowfall.
In the UK, Heathrow Airport said it would continue to run only 30% of flights until 0600 GMT on Wednesday.
At London St Pancras rail station the queue for Eurostar trains to France and Belgium stretched for about 1km.
Eurostar urged passengers to rebook or get a refund for their tickets, after services were curtailed by speed restrictions put on the lines.
The rail firm said it hoped everyone who needed to travel would get a place on a train, but staff estimated passengers would have to wait for four or five hours.
Meanwhile, at Eurostar's terminal in Paris, there were no reports of queues.
A spokesman for Frankfurt airport said 139 arrivals and 136 departures had been cancelled on Tuesday morning.
The airport has fully reopened, but delays were expected for most of the day.
Many people spent the night on camp-beds at the airport, where authorities brought in four brightly coloured clowns late on Monday to try and lift the mood in the terminals.
Airlines in Germany have been encouraging their passengers to take the train, while train operators - whose services are already overcrowded - urged passengers to stay at home, Reuters reports.
One frustrated passenger, 20-year-old Kristian Schuhmacher, said he had given up trying to fly to the UK.
"I have been trying to get back from Germany to the UK [to see] my parents since Friday. I have had five flights cancelled from both Frankfurt and Dusseldorf airports," he told the BBC.
He said he was going to drive to the UK instead.
French officials said the worst of the weather, which had badly affected road and air traffic, had begun to ease on Tuesday.
Transport ministry official Thierry Mariani said staff at Paris's main airport, Charles de Gaulle, were working round the clock to clear the backlog of flights.
And Brussels airport said it was able to operate more flights than expected.
The airport had earlier warned it expected to close for the day because of a shortage of de-icing fluid.
In the UK, there was growing discontent at the continuing failure to deal with the weather at Heathrow.
Late on Monday - 48 hours after the last heavy snowfall in London - passengers with tickets were turning up at Heathrow Airport only to be turned away from the already overcrowded hub.
Heathrow has published a list of flights that are expected to run on Tuesday.
The chaos at Heathrow has had a knock-on effect in other international hubs, where stranded passengers began to accept the possibility of not being with their loved ones over the Christmas period.
"My daughter is coming home and I don't see her very often and she's coming home to an empty house and it's just devastating," said 64-year-old Vivian Crosby, of Cambridge, England, stranded at New Jersey's Newark airport.
London Mayor Boris Johnson also expressed his frustration with the situation.
"It can't be beyond the wit of man surely to find the shovels, the diggers, the snow-ploughs or whatever it takes to clear the snow out from under the planes, to get the planes moving," he said late on Monday.
Airport operators explained that the sheer volume of snow - 12.7cm (five inches) in just one hour on Saturday - led to extensive ice build-up around aircraft on the ground and that safety concerns remained their priority.
The treacherous conditions are costing British Airways some £65m ($100m; 75m euros) a day, analysts say.
KLM-Air France said the weekend's disruption had cost it about 15 to 20m euros.