Written By: Ben Mutzabaugh, USA TODAY

Updated Thursday 3 p.m. ET. Next update: Thursday, by 7 p.m. ET.

UPDATE: A major winter storm is snarling flights in Chicago and elsewhere in the Midwest Thursday, a disruption that comes at the beginning of the busy Christmas travel rush.

More than 350 flights have already been canceled Thursday just at Chicago's two airports, and that number appears likely to grow.

Southwest, which flies the most domestic passengers of any U.S. airline, says it is suspending all of its flights at Chicago Midway as of 4:30 p.m. CT and at Milwaukee as of 5 p.m. CT, Southwest spokeswoman Olga Romero tells Today in the Sky. The service suspension includes flights on Southwest subsidiary AirTran.

The airline already had suspended operations this morning at Kansas City, but plans to resume service there after 2 p.m. CT (3 p.m. ET).

Southwest is the top carrier at Chicago Midway and has a major presence at Milwaukee, where it also is the top carrier if flights at subsidiary AirTran are included. Southwest's cancellations will have a significant impact on flight schedules at both airports.

Southwest, like most other big airlines, has instituted a flexible rebooking policy that allows most customers flying into the storm's path to make one change free of charge.

But, for those who are sticking to plans to fly today, the Midwest is a trouble spot.

Flights bound for Chicago O'Hare - the USA's second-busiest airport - are facing delays of up two hours because of strong winds ahead of the storm, according to the Federal Aviation Administration's flight delay map.

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Earlier today, the Chicago Department of Aviation put the number of storm-related cancellations at O'Hare more than 200 flights so far today. At Midway, the number was more than 150, according to the agency.

O'Hare is a major hub for both United and American, meaning this morning's disruption could ripple out and affect fliers at other airports.

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United, the nation's No. 1 global carrier and the biggest at Chicago O'Hare, says it alone had canceled about 125 United and United Express flights throughout the Midwest as of 11 a.m. CT, according to United spokeswoman Mary Clark.

Clark says the majority of those cancellations came at Chicago O'Hare, though some came on flights at United's other hubs on routes to smaller Midwest cities. Regardless, Clark says United is bracing for more.

"We do anticipate there will be more cancellations later today because of the way the storm is moving in," Clark says.

Unlike Southwest, however, Clark says United does not plan to halt flights altogether at Chicago.

She urged customers to check the status of their flight online before heading to the airport. Another options, Clark says, is United's relaxed rebooking policy that allows fliers scheduled to alter their flights in an attempt to avoid the storm.

For those whose flights are canceled, Clark says United will work to get them on other flights to their destinations.

"We are committed to doing everything we can to get passengers where they want to go for the holidays," Clark says.

At Chicago's Midway Airport this morning's problems were less severe than at O'Hare, though Southwest's evening cancellations will reduce the airport's late-day schedule to a virtual trickle.

The problems come from a blizzard that's strengthening as it moves into the Midwest, and conditions are expected to deteriorate for air travelers today across much of the Midwest. That includes Chicago, where heavy rain is expected to switch to ice and snow sometime around 6 p.m. local time.

Already, the storm has snarled flights at several mid-sized Midwest airports. At Des Moines, for example, the airport's online flight information page shows that all but two of this morning's departures there have been canceled. At Omaha, more than a dozen of the airport's morning departures had been canceled as of 7 a.m. local time, according to FlightStats. However, the weather began to improve in both cities by late morning.

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Elsewhere, a number of other airports - including those in Cedar Rapids (Iowa), Green Bay (Wis.), Madison (Wis.) - have reported at least a handful of cancellations so far this morning.

Unfortunately for fliers, the storm is expected to bring worsening blizzard conditions to much of the region today.

Flight schedules at Milwaukee's busy General Mitchell Airport have generally held up well through the morning, but the airport's website shows at least a dozen cancellations now on the board for this afternoon and evening.

The storm is even bringing problems to the South, where a long line of thunderstorms ahead of the storm could block flight paths in that region.

Hour-long delays at Memphis - a hub for Delta - had been reported earlier this morning by flight-tracking service FlightAware, though those problems appear to be easing. Current arrival delays there were averaging 27 minutes as of 2 p.m. local time, according to FlightAware.

In Atlanta, travelers flying through the world's busiest airport should pay attention to those storms as they develop.

The greatest risk from those storms is expected to come early to mid-day Thursday. However, the delay threat depends on whether the storms remain in a north-south "line" long and solid enough to block flight paths west of Atlanta. The threat of those storms is expected to dissipate by 5 p.m. ET.

Unfortunately for holiday fliers, the winter storm could extend its role as Grinch into the weekend.

Detroit, one of Delta's busiest hubs, is expected to see rainy, windy conditions today. The precipitation is forecast to switch to snow, though accumulations are expected to be minimal. Detroit's airport typically handles winter weather well, but given the disruptions elsewhere travelers flying to, from or through the city should monitor conditions and check ahead on the status of their flights.

Similar advice applies to fliers passing through Cleveland, a busy hub for United, which faces a similar forecast for Friday.

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With the edge of the storm forecast to move into the Northeast by Friday, the main concern for air travelers will turn to New York. Snow is not yet in the forecast there, but the predicted gusty winds, clouds and occasional rain are a bad mix for the metro area's delay-prone LaGuardia, JFK and Newark airports. Forecast winds also would bring the risk of sporadic delays at those airports on Saturday.

Even ahead of the storm's arrival, Newark and JFK flights were hit with delays by up to two hours on Wednesday as moderate winds buffeted the airports. Such delays could crop up all over again as the storm moves into the Northeast.

Winds also could disrupt flights Friday and Saturday in Philadelphia, though any problems that develop there are likely to be more sporadic.

As always, customers flying over the busy Christmas holiday travel period should check ahead on the status of their flight, and keep in mind that fair skies at their destination don't mean that they're immune from weather delays. For example, a flight from Charlotte to Dallas could become delayed or canceled if the aircraft or crews scheduled to operate the flight gets stuck in snowy Wisconsin.

Next update: Thursday, by 7 p.m. ET.

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