Canada’s Atlantic coast was also hit by the storm – the fourth in as many weeks to buffet the region.
Flights have now resumed into and out of New York, Boston and Philadelphia.
But many passengers were expected to be stranded until the end of the week after some 7,000 flights were cancelled over the busy holiday travel period.
Forecasters are now predicting milder weather for the rest of the week.
With many flights already expected to be nearly full between Christmas and New Year, airline industry experts said it would be difficult for companies to accommodate all the stranded passengers in the New York area quickly enough.
“This is a bad time for a blizzard to hit the east coast,” airline consultant Darryl Jenkins told the Associated Press news agency.
American Airlines spokesman Ed Martelle said his company could resume a normal flight schedule by Wednesday, but he was unable to say how long stranded passengers might have to wait for a flight.
“Any airline scheduler will tell you it’s like playing with a jigsaw puzzle where all the pieces keep changing shape,” Mr Martelle added.
Three airports serving New York – JFK, La Guardia and Newark Liberty International Airport – and also Boston’s Logan and Philadelphia International reopened on Monday evening.
They had been closed since early morning, forcing thousands of passengers to camp out on floors in terminals. Analysts say the storm and its aftermath could cost the airlines up to $100m (£64m).
Tens of thousands of homes were left without power. The New York Times quoted utility companies as saying homes in Massachusetts, New York City and Westchester County, Long Island and New Jersey had no supply.
In Canada, about 29,000 homes in Nova Scotia and New Brunswick were reportedly still without power early on Tuesday morning, although service had been restored to thousands of homes that were left without electricity during the height of the storm.
Five deaths were reported in road accidents in the storm, four in the Carolinas and one in Maine, the New York Times said, while many roads and streets remained blocked with snow.
National rail operator Amtrak – which earlier shut its New York-Boston route – announced a limited resumption of services.
The US National Weather Service said the monster snow storm was the result of a low pressure system which originated off North Carolina.
Six US states – Massachusetts, Maine, Maryland, New Jersey, North Carolina and Virginia – earlier all declared emergencies.
The New York area received up to 51cm (20in) of snow over two days. A subway train in New York City was trapped for seven hours before passengers were rescued.
The southern states of Georgia and South Carolina had their first white Christmas in more than a century.
But Washington DC escaped the blizzard, with only a dusting of snow.
The storm moved to Canada’s Atlantic coast early on Monday.
The timing of the snowstorm meant disruption for many thousands travelling after Christmas reunions. It also hampered the start of the shopping sales season and the return to work for many commuters – BBC