NEW YORK — A sloppy late-season storm lashed the Northeast with sleet and more than a foot of snow in some places Monday, paralyzing much of the Washington-to-Boston corridor after a remarkably mild February had lulled people into thinking the worst of winter was over.

The powerful nor’easter grounded more than 5,000 flights, knocked out power to over 100,000 customers from Virginia to Pennsylvania, closed schools in cities big and small and prompted dire warnings to stay off the roads.

As the morning wore on, the storm track shifted slightly and snow switched to sleet in Philadelphia and New York. Blizzard warnings were lifted in some places along the coast, and forecasts of a foot or more of snow were cut in half.

But residents farther inland were getting clobbered with snow.

“The winters seem to be upside down now. January and February are nice and then March and April seem to be more wintry than they were in the past,” he said Bob Clifford, who ventured out on an early morning grocery run for his family in Altamont, near Albany, New York.

The flight cancellations included more than 2,800 in the New York City area alone, where about 200 passengers were stranded at Kennedy Airport. Amtrak canceled or modified service up and down the Northeast Corridor. And the above-ground portions of the New York subway system were being shut down.

In the nation’s capital, the federal government announced a three-hour delayed arrival for non-emergency employees, with an option to take the day off or telecommute. Emergency employees were told to report on time unless otherwise directed.

“Good day to make brownies … and or read a book,” said Gov. Dannel P. Malloy of Connecticut, which was expecting up to 2 feet of snow in some areas.

New York Gov. Andrew Cuomo declared a state of emergency for the entire state and instructed non-essential state employees to stay home.

In Massachusetts, where the forecast called for 12 to 18 inches of snow, Gov. Charlie Baker encouraged motorists to stay off the roads and to take public transit only if absolutely necessary, saying the fast snowfall rates would make driving hazardous.