Prime Minister David Cameron said today he was "frustrated" by the continued disruption at Heathrow as the Government offered military support to help clear the snow.
While thousands of air passengers remained stranded, rail travellers were also hit by widespread disruptions, with hundreds of people evacuated from stricken trains.
The East Coast line, one of the country's main railway arteries, was suspended between London and Peterborough with passengers advised to stay at home.
And with Christmas the busiest travel period of the year, the AA was preparing for increasing problems on the roads.
Speaking at a Downing Street news conference, Mr Cameron said: "If it's understandable that Heathrow had to close briefly, I'm frustrated on behalf of all those affected that it's taking so long for the situation to improve.
"There have been intensive discussions between (Transport Secretary) Philip Hammond and BAA about how best to ensure that normal flying capacity is resumed as soon as possible.
"I can tell you now that snow ploughs are on that second runway as I speak and the second runway will be open by this evening."
He added: "The people stuck there are having an incredibly difficult time, especially just a few days from Christmas, and everything must be done to either get them on holiday or get them home safely."
Heathrow said it will operate about a third of scheduled flights until at least 6am on Thursday.
Passengers were urged to check the airport website to see if their flight was listed for departure and then confirm with the airline before setting off.
BAA chief executive Colin Matthews and BAA chairman Sir Nigel Rudd met Mr Hammond at Heathrow.
Mr Hammond told Sky News: "What we're trying to do now is focus our entire energy on providing BAA with the maximum support to get as many passengers away as possible before the holiday weekend.
"We've offered BAA the use of troops if they need additional manpower for snow clearing although they tell us they've actually got the manpower they need here."
There were also flight disruptions at Aberdeen, Edinburgh and Glasgow, as well as Gatwick, London Luton and London City airports.
The EU Commission slammed Europe's air travel disruption as unacceptable and urged airports to "get serious" about better planning for bad weather.
Meanwhile, hundreds of passengers were evacuated from trains earlier in the day following damage to overhead power lines at Huntingdon near Peterborough.
A total of eight trains were affected, with five of these reaching stations for passengers to disembark.
But about 200 people were forced to climb down onto the tracks when an East Coast service ground to a halt, and about 80 more passengers from two First Capital Connect services also abandoned carriages.
The trouble followed an incident overnight in which more than a hundred people were stuck for six hours on a train in Kent when lines froze.
Southeastern said the train, from London Victoria to Ashford, was stranded between Kemsing and Otford after heavy snowfall. The travellers were eventually rescued at 3am after another train was sent alongside as a "last resort".
Eurostar was operating a reduced service with the company asking customers not to travel unless essential.
Speed restrictions were in place on its high-speed lines, adding up to two hours to journey times.
The rail company said: "We are asking all customers booked to travel before Christmas to refund or exchange their tickets free of charge if their travel is not essential."
Disruptions also affected rail services including Northern Rail, London Midland, Chiltern, Virgin, ScotRail and First TransPennine Express.
Robin Gisby, Network Rail's director of operations and customer services, said: "I must apologise to passengers using services on the East Coast today. I have scores of engineers on site fixing the overhead power lines and I expect some limited services to resume later this evening and a full restoration for the morning."
Michael Roberts, chief executive of the Association of Train Operating Companies (Atoc), said: "Across the country, the vast majority of trains have continued to run and most have arrived on time. However, there has been disruption today and we apologise to any passengers who have had trouble getting to where they want to go.
"Network Rail and train companies will continue to work flat out through the coming days and nights to keep as many services running as possible in the run-up to Christmas."
The AA, which yesterday experienced its busiest ever day, was dealing with 2,000 breakdowns an hour, twice the normal rate.
Darron Burness, head of AA Special Operations, said: "Daytime temperatures have continued to remain below freezing in many areas today and we're still seeing some perishingly cold overnight lows. Although the outlook is better for the latter half of the week, it is still December, so will hardly be tropical - ice will remain a risk, especially when dark."
Andy Ratcliffe, forecaster at MeteoGroup, the Press Association's weather division, said Heathrow and Gatwick could expect temperatures of 1-2C tomorrow.
Overnight a band of snow was set to develop through Wales, East Anglia and the Midlands, with the possibility of heavy snow early tomorrow.
"We're not expecting any snow after tomorrow at Heathrow and Gatwick but temperatures will stay cold so there will not be a rapid thaw," he said.
"The cold spell will keep its grip on the country at least until the weekend."