Heathrow had already cancelled 111 flights on Saturday.
As hundreds queued at check-in desks at Heathrow, passengers were told not to join queues unless their flight was within two hours.
Of the 111 cancelled flights, 101 of them were with British Airways (BA).
Air France, Aer Lingus, Lufthansa and TAP Portugal flights have also been affected.
“Latest forecasts for tomorrow show a high probability of around 2-6cm of accumulating snow and low visibility at periods throughout the day,” a Heathrow spokesman said.
“This will reduce the capacity of the airport and without action would cause significant disruption to passengers and flights.”
Sleeping in airport
Details of which flights will be cancelled will be announced by airlines when they have finalised their schedules, the airport said.
A statement from BA said: “We are doing everything we can to help customers whose flights have been disrupted by severe weather and we fully apologise for the inconvenience caused to their travel plans.
“Like other airlines at Heathrow we have complied with a request to reduce our schedule by 20% on Sunday and we continue to work with Heathrow Airport to help keep the airport running as smoothly as possible.”
BA said it will try to give customers “as much notice as possible”.
On Friday more than 400 flights were axed and thousands of passengers ended up sleeping in the airport.
The spokesman added that in low visibility more space needs to be left between aircraft, which was difficult at Heathrow as it runs at almost full capacity – therefore delayed flights could not be rescheduled.
In other developments:
Some passengers queuing for hours were clearly upset about the uncertainty while others seemed to be taking it in their stride.
A 26-year-old woman, who was supposed to fly with her mother to Hong Kong, was crying while on her mobile phone. The pair did not want to be named.
The mother said: “She thought that it was all going smoothly.
“The bad thing is the baggage. All baggage went through and they wouldn’t let them have it back.”
Danish transit passenger Ebbe Bernhagen, who is heading to San Francisco with his wife, said: “I’ve been in the queue for three and a half hours.
“I sat on the plane for five hours in Copenhagen.”
But one Australian man on his way to Geneva, who did not want to be identified, saw the lighter side of the chaos.
“We’ve spoken to more reporters than BA staff,” he said. “Does it come as a great surprise that it snows in the northern hemisphere?”
On Friday passenger Ian Aitchison, who was due in the US for a conference, said he was on a plane for more than six hours before the flight was cancelled and he was then told he would be unable to get his luggage back and has to arrange to have it sent later.
“It’s pretty funny. To be honest I’m mildly hysterical… obviously there’s a lot of people who are quite upset.”
Jamie Methuen was supposed to fly to Geneva on Friday and then travel to France for a skiing weekend.
He told the BBC his flight was cancelled after a four-hour wait at Heathrow, and that he would have “appreciated a far more honest and pragmatic approach” from the airlines, “four hours earlier”.