Separately, Swedish weather agency SMHI's latest forecast shows that snow will likely cause problems for travellers across the country during the Christmas holidays.
Scandinavian airline SAS' biggest problems involve flights in London and at Heathrow.
"It is the absolute worst there. From Frankfurt and Paris, things are running smoothly and we are getting passengers out. In London, we currently have about 5,000 to 6,000 SAS customers, but not all of them are going to Sweden. About 2,000 are going to Landvetter or Arlanda, said SAS information director Elisabeth Manzi.
"The remainder are heading to destinations in Denmark and Norway. The problems in London stem from Heathrow being closed for a longer time than the other large airports on the continent," she added.
The cancelled flights have forced a number of affected travellers to scrap their Christmas plans, while others are racing to salvage the holidays by coming up with alternative ways home, including taking buses to Copenhagen at their own expense.
Travellers have complained that SAS has offered them no help at all, saying that they have been told that they are responsible for their own arrangements.
SMHI changed after lunch on Tuesday its weather forecast for Thursday and Christmas Eve, saying that snowfall over southern Sweden is expected to extend further east out over the Baltic Sea.
"It is now set to really pick up on Saturday and snow over southern and eastern Götaland, as well as eastern Svealand. The largest volume will fall over Gotland and along the Baltic Sea provinces," said Anna Hagenblad, meteorologist at SMHI.
"The snowfall on land could be less. Most of the snow will fall over the Baltic Sea," she continued, adding that the forecasts are still very "disconnected."
Even if there is less snow than expected over southern Sweden on Thursday and Friday, there is still a risk of regular traffic problems.
"There will possibly be a warning on Friday (Christmas Eve) and it depends on the combination of snow and wind," said Hagenblad.
In connection with the snowfall, temperatures are expected to rise to -5 to -1 degrees Celsius in the southern parts of the country and -10 to -5 degrees Celsius in the northern parts of Götaland and Svealand.
SMHI has issued class 1 warnings on a rising scale of one to three for Blekinge and parts of northeastern Sweden, where up to 10 centimetres of fresh snow are expected to fall on Tuesday.
National rail operator SJ estimates 1 million passengers will travel by train during the Christmas holidays and has already admitted to not having enough resources to cope, especially if the weather causes problems.