Schools are closed and thousands of flights have been cancelled.
The conditions caused German Chancellor Angela Merkel to postpone a trip to Washington to meet President Trump.
With winds of up to 60mph (100km/h), Winter Storm Stella is likely to cause severe disruption for commuters across many parts of the north-east, forecasters say.
In all, about 50 million people across America are under a blizzard warning.
A 24-hour blizzard warning was issued by the US National Weather Service from midnight (04:00 GMT Tuesday) for New York, Connecticut and New Jersey.
"Snowfall amounts in excess of a foot are likely inland along with strong and gusty winds," the agency said.
Winter storm warnings were also posted from eastern West Virginia to Maine.
"During its height we could see snowfall rates of 1-3 inches (2.5-7.6cm), even up to four inches per hour," said Alan Dunham, a meteorologist based in Taunton, Massachusetts.
More than 6,800 flights have been cancelled, tracking service FlightAware reported, with airports in New York, Washington, Boston, Baltimore and Philadelphia worst hit.
Schools will be closed on Tuesday in New York, Providence, Rhode Island and in some towns across Massachusetts and Connecticut.
Declaring a state of emergency, New York Governor Andrew Cuomo said commuters should expect road closures, delays and cancellations.
"I strongly urge everyone to limit unnecessary travel on Tuesday and if you must drive, please plan ahead, be careful, and stay safe," he said in a statement.
Mr Cuomo advised New Yorkers to prepare food supplies for seven to 10 days, and an emergency supply of bottled water.
New Jersey Governor Chris Christie also declared a state of emergency and ordered all state employees not involved in the response to stay at home.
Mrs Merkel's visit, which was planned for Tuesday, has been rescheduled for Friday.
The storm also forced Irish Taoiseach (Prime Minister) Enda Kenny to cut short a visit to Boston and head to Washington a day early by train.
The winter storm follows a spell of unusually mild weather in the north-eastern US, with last month being the second warmest February since record-keeping began in 1895.
President Trump said he had spoken to Homeland Security and that the Federal Emergency Management Agency was ready to provide assistance where needed.
"Everybody in government is fully prepared and ready," he said. "Let's hope it's not going to be as bad as some people are predicting. Usually it isn't."
In 2016 New York experienced the biggest snowstorm in the city's history, with a record 27.3 inches falling on Central Park in 24 hours.
The blizzard brought parts of the north-eastern states to a standstill, and left 18 people dead.
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