Up to seven inches of snow was expected by Thursday on hard-hit Staten Island while parts of Connecticut reported more than 8 inches of snow fell overnight, CNN reported.
"It's Mother Nature's one-two punch," Newark, N.J., Mayor Cory Booker told CNN. "It's testing the resolve and the grit of my state and my city and, obviously, this region."
About 25,000 Newark residents were still without power from Sandy.
"Now, this is being dumped. It has the potential to knock out more power within my state," Booker said.
Parks, playgrounds and beaches in New York City were to remain closed through Friday because of the storm, NBC News reported.
Power outages in New York and New Jersey rose from 607,000 customers Wednesday to 666,000 customers by early Thursday.
"We're getting hit pretty hard between the snow and the wind," Long Island Power Authority spokeswoman Elizabeth Flagler said.
Weather forecasts indicated wind gusts as high as 60 mph along shore communities in New York and New Jersey, along with 2- to 4-foot foot storm surges just as Sandy-generated floodwaters had begun to recede.
A gale warning was in effect for much of the northeast coast, the National Weather Service said.
New York Mayor Michael Bloomberg had urged residents in low-lying areas to consider spending Wednesday night elsewhere, but didn't issue mandatory evacuation orders except for a few chronic-care facilities and an adult care center in areas hit hard by Sandy.
In New Jersey, the Brick Township Office of Emergency Management issued a mandatory evacuation order for residents of the town's low-lying waterfront areas.
At least 300 flights were canceled Thursday at New York-area airports, the New York Daily News reported. More than 1,500 flights were delayed or canceled at Kennedy, LaGuardia and Newark airports Wednesday.
More than a week after Sandy struck the Northeast and mid-Atlantic states, the storm-related death toll in New York City rose to 41 as a 78-year-old man died Tuesday of injuries he sustained during the storm, police said. The superstorm killed at least 111 people in the United States and knocked out power to millions of customers.