Tuesday's storm has been followed by bitter cold temperatures and below freezing wind chills so the snow won't melt quickly.
Motorists are advised to slow down and pedestrians are urged to use caution because roads and sidewalks are icy.
Many schools are closed and state government offices also are closed Wednesday.
Most of the snow fell in Monmouth, Mercer and Middlesex counties. Manalapan is reporting nearly 16 inches, East Windsor saw 12 inches and Piscataway received 10 inches.
New Jersey Transit trains are operating on an enhanced weekend schedule. Buses and trains are cross-honoring tickets.
New Jersey remains under a state of emergency after Gov. Chris Christie's formal declaration on Tuesday.
The winter storm socked New Jersey with snow and gusty winds, turning the afternoon commute into a tangled mess and forcing hundreds of cancellations at area airports.
Christie made the announcement early Tuesday afternoon as snow continued to fall steadily across most of the state. Travel conditions were expected to worsen as the day progressed, and drivers were being urged to allow extra travel time or postpone their trips if possible.
Across the state, commuters choked the streets by early afternoon, hoping to get a jump on the traffic home, but numerous traffic backups were reported on major and local roadways. To help ease the congestion, New Jersey Transit buses and trains were cross-honoring tickets.
By late Tuesday afternoon, state police said there had been 238 reported motor vehicle accidents and 354 incidents where motorists needed aid.
The storm forced Christie to cancel his inaugural party scheduled for Tuesday night on Ellis Island.