The Christmas travel plans of thousands of Britons are in disarray after snow left Heathrow Airport all but shut.
Thousands remained in terminals for hours as few flights departed on Sunday. Knock-on delays hit most UK airports, including Gatwick.
The Met Office warns of more heavy snow in Yorkshire, north-east England and eastern Scotland, advising essential travel only in the Edinburgh area.
Icy roads affect much of the rest of the UK. There is some rail disruption.
An extreme weather warning is in place for Edinburgh, Lothian and Borders, with some 15 to 20cm (6-8in) of snow expected between 1100 and 1800 GMT.
Up to 10cm (4in) are expected in other snow-affected areas, with up to 20cm on high ground.
Edinburgh airport was closed until 1430 GMT and then opened for departures only on Sunday.
Temperatures struggled to get above -5C (23F) overnight and BBC forecaster Matt Taylor said there were lows of -19C (-2F) in parts of Worcestershire and Shropshire. They are likely to stay below freezing throughout the day.
The Met Office also issued warnings of heavy snow in parts of Sussex, East Sussex and Kent on Sunday.
Trains between London and Peterborough were suspended late on Sunday due to problems with overhead wire problems, train company East Coast said.
No trains are running between Oxford and Hereford, while some Chiltern Railways, South West Trains and First Capital Connect services have been weather-affected.
With France also suffering severe weather, Eurostar said it had cancelled some trains and switched to a contingency timetable, with last-minute cancellations possible. Speed restrictions were adding an additional 90 minutes to journeys.
Drivers are facing queues of up to eight hours on the A34 in Oxfordshire, where more than 80 cars were abandoned on Saturday night and several jack-knifed lorries were blocking the route. The nearby Cherwell Valley services on the M40 has run out of fuel.
The M25 has re-opened after being closed in both directions between junctions five and six, causing long delays following a liquid petroleum gas tanker overturning at 0900 GMT.
But airports were worst hit, on a weekend when travel association Abta said hundreds of thousands of Britons were due to fly.
The BBC has received hundreds of e-mails from stranded passengers, with many saying they have no idea where they will be spending Christmas.
BA said "several thousand" of its stranded passengers were being put up in hotels but when asked if the company was confident of getting everyone to their festive destinations, a spokeswoman said: "We are in the hands of the weather."
People are advised against travelling to Heathrow Airport, which said "a few thousand" spent the night in the terminals. Just four short-haul and three long-haul flights left on Sunday morning.
By late on Sunday night, BAA said three flights had landed at Heathrow, with more maybe due later.
The airport earlier said it hoped to be operational on Monday, but warned of more cancellations and delays "in the days that follow" as airlines move diverted aircraft and crew back to their normal positions.
Sue Kerslake spent the night on a terminal floor with her three young grandchildren after their Cathay Pacific flight to Hong Kong was cancelled.
"There were thousands of people in departures overnight and it got quite intense at times. The bars were open and some people were drinking and got quite nasty," she said.
Stuart Gash, from Swindon, who had been due to fly to New York for a Caribbean cruise with his wife and two children, said UK airports seemed unable to cope at the first sign of snow.
He said: "There was no more than two inches of snow and yet the runway is totally covered. Why aren't they ploughing it, why aren't they gritting it, why aren't they salting it?"
Andrew Teacher, from Heathrow operator BAA, said it had invested more than £6m in the last year in technology to move snow and de-ice runways and that staff had worked through the night.
But he said: "There comes a point where you cannot do any more; when you're moving snow and it's freezing behind," adding that many planes had been frozen into parking spaces.
He apologised for the "miserable" situation but said problems had been caused by "an extreme amount of snow in a very short space of time" and safety had to be prioritised.
Hundreds of staff had been drafted in to hand blankets, food and water to passengers stuck in terminals, he added, but many still complained to the BBC they had been left without.
The Independent's travel editor Simon Calder said very few of the 400,000 passengers due to fly out of Heathrow this weekend would get to their destinations. At Gatwick, 90,000 people should fly out on Sunday but 50 fights are cancelled.
A Gatwick spokeswoman said it was doing everything it could to "get passengers on their way" but advised them to check with airlines before setting out.
Infrastructure 'seized up'
Aberdeen airport re-opened again at about 1600 GMT. It had managed to open for just under three hours in the middle of the day, but had closed by 1500 GMT for another hour of snow clearing, BAA said.
The runways at Jersey and Guernsey airports remain closed.
Stansted, Luton, Exeter, London City, Birmingham, Bristol and Southampton airports said flights would be subject to delays and cancellations throughout Sunday.
Belfast International Airport has reopened after some of the heaviest snowfall for 25 years, although knock-on effects have caused delays.
Ryanair has cancelled 84 flights to or from UK airports, mainly in the London area.
Monarch Airlines managing director Tim Jeans said reassessment of the UK's transport capabilities was needed.
"We have not coped well. The infrastructure - not just at the airports but the road infrastructure - completely seized up. The M25 going towards Heathrow and Gatwick virtually impassable within an hour of the snow starting to fall."
Transport Secretary Philip Hammond has asked the government's chief scientific adviser for advice on whether the government should be planning for more severe weather in future.
"The question I'm asking him is whether we should go on assuming that an extreme weather event is something that will happen perhaps once every few years and just recognising that we just can't invest large amounts of money preparing for it, or whether it is something now that we have to assume will happen perhaps two or three times a year."
But shadow transport minister Maria Eagle accused him of complacency.
"We had a winter resilience report which was ordered by the previous government on his desk in July and he could have started by implementing the recommendations," she said.
- Despite problems in some areas, National Rail Enquiries says most routes are operating normally and advises passengers to call 08453 017 641 for details
- The AA said it expected to have attended around 14,000 call-outs by the end of Sunday, double the number on a normal Sunday
- Sunday's sporting schedule was again badly affected, after wide postponements of football, rugby union and horse racing fixtures on Saturday
- An urgent appeal is being made for blood donors, particularly those who are O negative, as stocks are running low
- Companies have warned of a backlog of deliveries which may not reach customers before Christmas
The Highways Agency has said it is doing its best to keep major roads in England clear but that motorists should check traffic and weather conditions before considering whether to go out.
Wintry problems were also occurring on continental Europe.
Frankfurt airport, Germany's biggest, was open but hundreds of flights were again cancelled on Sunday because of problems elsewhere, leaving the airport halls "packed with flight guests," a spokeswoman told Reuters.
Heavy snow in northern France has led to air and train disruptions, with a quarter of flights cancelled at Paris's Charles de Gaulle and Orly airports.
The Tuscany region of northern Italy remains under heavy snow, and Florence airport was closed.
Amsterdam's Schiphol airport was open, but about 30 flights were cancelled on Sunday because other airports were closed.