More than 3,300 US flights were cancelled on Thursday as snow blanketed parts of New York and New England, as well as eastern Canada.
Boston could get up to 18in (45cm) of snow, while New York City is bracing for up 1ft, say forecasters.
The storm, known as a “bomb cyclone”, is expected to continue to affect eastern North America into the weekend.
Nearly 60 million people are in the path of the storm, with weather warnings in effect from the Maine to parts of Georgia in the US.
The National Weather Service said: “Heavy snowfall rates will spread northward across NH and through southern/central ME through early this evening.
“In addition to heavy snowfall rates, the intensifying storm will result in strengthening winds, producing blizzard conditions for coastal regions of New England.”
Hurricane force winds of up to 60mph (95km/h) are expected to hammer the north-eastern US coastline.
US railway operator Amtrak is running on a reduced schedule, and interstate buses are also being cancelled.
The weather pattern has already brought snow to the US South as far down as Florida.
“The situation has continued to deteriorate,” said New York Governor Andrew Cuomo as he declared a state of emergency on Thursday.
“It’s almost impossible to clear roads when you have those high wind gusts, because as soon as you clear the road the snow, the wind literally just brings the snow back on to the road.”
Cars becoming stranded on the Long Island Expressway, he added, could cause a “situation of life and death” in which rescuers may be unable to reach trapped motorists.
Seventeen cold-related deaths have been reported across the US, according to the Associated Press news agency.
Three people were reported dead in Texas due to the cold temperatures.
Two people were killed in North Carolina when their pickup truck ran off a snowy road and overturned in a creek in Moore County, which had not expected snowfall, according to Governor Roy Cooper. An additional traffic-related death was also reported in Beaufort.
A “bomb cyclone” or “weather bomb” is an unofficial term for what is known as explosive cyclogenesis, according to BBC Weather.
This occurs when the central pressure of a low pressure system falls by 24 millibars in 24 hours and can result in violent winds developing around the system.
The winds can be strong enough to bring down trees and cause structural damage.
The storm is forecast to undergo rapid cyclogenesis over the Atlantic Ocean throughout Thursday and into the weekend, and current projections show areas north of New York as having the highest risk of significant impacts from strong winds and heavy snow.
Images online show floating ice floes on Mississippi River piling up under bridges.
Four Thresher sharks, which conservationists say are particularly vulnerable to the cold, have been found frozen to death along the Cape Cod Bay shoreline in Massachusetts.
Schools are closed in New York City, Philadelphia, Boston, the Carolinas, Maryland, and Virginia due to the danger of hypothermia, frostbite and traffic accidents.
Photos went viral online of students attending a lesson at a public school with a broken furnace in the Maryland city of Baltimore.
The entire Baltimore City public school system closed down after the local teachers’ union complained of its educators being “forced to endure teaching in classrooms with dangerously low temperatures, instructing students who have been forced to try to learn bundled up in coats, hats and gloves”.