HARTFORD, Conn. — Light snow was falling Thursday in parts of the Northeast as a winter storm bore down on the region, promising significant snowfall, strong winds and frigid temperatures that will make commutes hazardous for the first work day of the new year.

Snow began falling overnight in parts of New England and New York, but the real brunt of the storm wasn’t expected to hit until later Thursday. As much as a foot of snow or more was forecast for some areas overnight Thursday into Friday, and temperatures were expected to plummet, with some areas seeing highs just above zero, according to the National Weather Service.

“There will be travel problems,” said Hugh Johnson, a weather service meteorologist in Albany, N.Y. “It will be very cold.”

Up to 14 inches of snow is forecast for the Boston area and the National Weather Service issued a blizzard warning for Long Island — where 8 to 10 inches of snow could fall and winds could gust up to 45 mph — from Thursday evening into Friday afternoon.

Some schools in New England and New York closed pre-emptively or planned early dismissals, while cities issued on-street parking bans and homeless shelters were expected to fill beyond capacity.

The storm dropped up to a foot of snow on parts of Michigan and 6 inches or more in Illinois, prompting hundreds of flight cancellations Wednesday into and out of Chicago’s O’Hare International Airport, according to the aviation tracking website FlightAware.com. About 1,000 U.S. flights were canceled for Thursday, with O’Hare and New Jersey’s Newark Liberty International most affected.

Authorities said the weather may have been a factor in a fatal crash Wednesday evening involving a pickup and a bus carrying casino patrons in Indiana. Police said the truck’s driver was killed and 15 bus passengers were injured in the collision on a snow-covered and slushy highway in Rolling Prairie.

Sections of interior southern New England and New York could get up to a foot of snow by the time the storm moves out, with forecasts generally calling for 6 to 12 inches. New York City, likely to see 3 to 7 inches, issued a snow alert. New York Gov. Andrew Cuomo urged the city’s commuters to leave their cars at home in case major highways are closed for Thursday’s evening rush hour.