There were no injuries.
The plane was Delta Connection 4100. The FAA says the plane made a safe landing, but as it was exiting the runway onto a taxiway at about 8 a.m., it slid into a snowbank.
34 passengers and crew members were on board the flight.
Arrivals and departures at JFK were halted at 8:30 due to the icy conditions created by freezing rain.
Meanwhile, passengers on other flights wished Sunday was just a bad dream. All flights in and out of Kennedy were stopped for two hours.
"I've been here since 6 o'clock this morning, and I'm just trying to get back home to Fort Lauderdale, Florida," said Sherieda Crockett.
Between the crowds, the cancellations and the overall conditions with rain and ice outside, this day was a rude awakening for anyone returning to the Tri-State area from someplace tropical.
The flight, flown by Endeavor Air, originated in Toronto. The plane was towed back to the gate to allow the passengers off.
The Port Authority says the incident is under investigation, and that the speed of the plane is being reviewed.
"It could have been worse, a much worse scenario," passenger Jordan Houlton told reporters after he emerged from the plane.
Houlton, a 27-year-old teacher in Mexico, said he managed to sleep through the slide and didn't learn until later that the plane had skidded off course.
"I was sleeping. I woke up and it was 9:30," Houlton said. "A police officer came on to make sure everyone was OK. Luckily, everyone was OK. It was kind of wild. I still can't believe it."