As Lindbergh Field was opening for departing flights just before 7 a.m., there was already bad news for some travellers.
American Airlines, United and Continental had canceled about a dozen flights combined. The board showed delays for other flights as well as of 7 a.m.
Delta canceled more than 625 flights across the country Tuesday.
JetBlue says it will cancel its flights in and out of New York's JFK airport beginning at 10 a.m. Tuesday, with some flights to resume Wednesday afternoon.
It plans to shut down its Boston flying on Tuesday night, resuming Thursday morning.
Dallas-Fort Worth International Airport closed for a time Tuesday morning due to icy runways.
DFW Airport spokesman David Magana said one runway has reopened and crews are working to clear the ice from others.
The airport, the eighth largest in the world, is the main hub for American Airlines.
Earlier Tuesday, hundreds of incoming flights were canceled due to the massive winter storm sweeping much of the country.
Get more coverage of the storm on MSNBC.com.