WASHINGTON, March 5 (Reuters) - A winter storm reaching from Texas to New England closed schools, canceled more than 3,400 flights and stranded hundreds of drivers overnight in Kentucky, where as much as 21.5 inches (55 cm) of snow fell.

A plane slid off the runway at New York's LaGuardia Airport, according to the New York City fire department. The Federal Aviation Administration said on its website that the airport was closed because of an "aircraft incident." There were no immediate reports of injuries.

Cancellations were announced for hundreds of school districts, government offices and legislatures in the District of Columbia, New Jersey, South Carolina and Tennessee.

Kentucky Governor Steve Beshear declared a state of emergency on Thursday.

"Help is on the way," Kentucky National Guard Lieutenant Colonel Kirk Hilbrecht, interviewed on CNN, told drivers stuck in their cars on I-65 as long as 12 hours.

Besides the cars, at least 200 tractor trailers were stuck on the roadway, which officials said was impassable, said Kentucky State Police Trooper Jeff Gregory.

Kaleigh Birman said she was headed from Michigan to Florida for a spring break holiday with her family when her carload of six people and two dogs got stuck overnight on I-65.

"We swerved in and out of parked cars," Birman told Reuters in a Twitter post, noting that the accumulation became so heavy it forced her car to a standstill, too. "I'm pretty sure everyone is running out of gas."

The stranded drivers were told on Thursday morning that it would take several hours to reopen the roadway and that National Guardsmen would assist them as well as drivers stuck on western Kentucky roads. The governor said the stranded vehicles were blocking first responders.

National Weather Service meteorologist Andrew Orrison said Kentucky was buried under snow, with 21.5 inches reported in the city of Radcliff and more than a foot falling elsewhere in the state.

Parts of Arkansas, Illinois, Indiana and Ohio recorded as much as 11 inches (28 cm) of snow, and freezing rain glazed Tennessee, Mississippi and Alabama, the weather service said.

After moving out of Kentucky, the storm bore down on West Virginia and northern Virginia, pelting New York City, Long Island and the southern parts of New England.

A total of 3,417 U.S. flights for Thursday were canceled, according to FlightAware.com, with airports in Dallas, Washington, Philadelphia and the New York metropolitan area hardest hit.

Boston might not get any snow from the newest storm, the weather service said. Only 2 more inches would break the city's record annual snowfall total of nearly 108 inches, which was set in the year that ended in June 1996. (Reporting by Curtis Skinner and Barbara Goldberg; Additional reporting by Tim Ryan and Ian Simpson in Washington,; Steve Barnes in Little Rock, Arkansas; and Steve Bittenbender in Louisville, Kentucky; Editing by Kevin Liffey and Lisa Von Ahn)