At least four deaths have so far been blamed on the storm, which is predicted to dump at least three feet of snow in some parts over the weekend.
Four airports were forced to close, a state of emergency was declared in five states, and roads in many places were rendered impassable, even to emergency vehicles.
An estimated 650,000 homes were said to have lost power while more than 5,300 flights, including some to and from Britain, were cancelled.
Blizzard warnings were in effect yesterday for much of the coastal section of the north-eastern US, from Newark, New Jersey, to southern Maine. People were warned in advance to stock up on food and other supplies, with the storm predicted to affect some 25 million.
Wind gusts could reach 75 mph and widespread power failures were feared, along with flooding in coastal areas still recovering from last year’s “Superstorm Sandy”.
More than three feet of snow fell in parts of Connecticut, and more than two feet were reported on Long Island and in Massachusetts.
Homes and businesses were left without power in large swathes of Rhode Island, Connecticut and Massachusetts, the latter two introducing state-wide driving bans.
Officials in Massachusetts ordered the evacuation of some communities along the coast as waves lashed the shoreline and high tides brought a surge of water inland.
Peter Judge, of the Massachusetts Emergency Management Agency, which brought in the National Guard to help evacuate people, said: “We had pre-positioned National Guard troops and equipment vehicles, basically along the south coast from the town of Hull, all the way to Cape Cod.”
The United States Postal Service closed its offices and suspended its deliveries on Saturday throughout New England, where residents were urged to stay indoors.
In Maine itself, officials said numerous vehicles, including several state police cars, were stuck in deep snow and warned stranded drivers to expect long waits for tow trucks or other assistance.
New York City’s three major airports and Boston’s Logan Airport were closed.
Heathrow Airport said 32 inbound flights from the US and two outbound flights were cancelled, leaving thousands of Britons stranded.
A nuclear power plant in Plymouth, Massachusetts, automatically shut down due to the heavy snowfall but the authorities there insisted there was no threat to public safety.
The US National Weather Service said the combination of two weather systems from the polar and sub-tropical jet streams would produce a “potentially historic” storm.
Meteorologist Alan Dunham said: “This one doesn’t come along every day. This is going to be a dangerous winter storm.”
The weather service said up to three feet of snow was expected in Boston, threatening the city’s 2003 record of 27∫ inches.
Boston mayor Thomas Menino said: “This is a storm of major proportions. Stay off the roads. Stay home.”
In downtown Boston, Santander bank employee Tommaso Memeghini, from Barcelona, was among those stranded after his flight back to Spain was cancelled.
“We are not believing it,” he said. “We were told it may be the biggest snowstorm in the last 20 years.”
Philip Gagnon, mayor of Gorham, in Maine, which was buried under more than 31 inches of snow, said it could take several days to get it moving again.
In Connecticut, governor Dannel Malloy said there were several cases of people stranded in cars who needed to be treated for hypothermia.
“One of the biggest problems we are facing is stalled automobiles,” he said. “We are trying to dig them out and tow them away.”
In Canada, New Brunswick, Nova Scotia and Newfoundland were under blizzard or storm watches yesterday.
By last night there had already been 200 vehicle accidents, claiming at least three lives.
In one incident, an 80-year-old woman collapsed while shovelling her driveway and two men were killed in car crashes. One man in his 70s also died when he lost control of his vehicle in New York.
Around 11 inches fell in central New York overnight, but the city was “in great shape”, according to mayor Michael Bloomberg, who vowed the streets would be cleared by the end of the day.
He added: “I think it is fair to say we were very lucky.”
Early snowfalls were also blamed for a 19-car pile-up in Cumberland, Maine, that caused minor injuries.
In New York, hundreds of cars began getting stuck on the Long Island Expressway on Friday afternoon at the beginning of the snowstorm and dozens of motorists remained trapped overnight as police worked to free them.
Richard Ebbrecht got stuck six or seven times on the Long Island Expressway and other roads.
“We were all helping each other, shovelling, pushing,” he said. He finally gave up and spent the night in his car, walking home at daybreak.
Snowplough driver Jack Mandaneza, who was working on the Long Island Expressway, said: “It’s really hard right now, it’s wet, it’s heavy and it’s freezing, so everything is going slow.”