The slow-moving winter storm, which forecasters have been warning about for most of the week, has finally arrived in southwestern Connecticut -- with the fluffy snow that started falling last night still coming down steadily this morning.

Several inches of snow have already accumulated in coastal regions of lower Fairfield County, and deeper snowfall is being seen farther inland.

Most school districts in the region had cancelled classes for the day by 6 a.m.

In a Winter Storm Warning that remains in effect until midday, the National Weather Service says the snow is expected to keep falling through about 1 p.m., then change to a mix of snow and rain, and after 4 p.m., the precipitation should be mostly rain. The daytime high temperature is expected to rise to the upper-30s, with a north wind 14 to 23 mph, with gusts as high as 38 mph. Chance of daytime precipitation is 100 percent, with snow accumulation of 4 to 6 inches possible.

There also is a Coastal Flood Advisory in effect through 10 a.m., with the greatest flooding threat during the high-tide period about 8 a.m.

Tonight should be cloudy during the early evening, then there will gradual clearing, the NWS says, with a low temperature in the upper-20s and a north wind 9 to 17 mph, with gusts as high as 30 mph.

Tomorrow there should a marked change in the weather, as skies turn sunny and the temperature rises to the upper-40s. Nighttime should be mostly clear, with a low temperature about 30 degrees.

Sunday also should be mostly sunny, with a high temperature near 50 degrees. Skies will be mostly cloudy at night, with a low temperature in the mid-30s.

On Monday, there is a chance of showers after noon as temperatures rise to the low-50s. Showers are also possible Monday night, with a low temperature about 40 degrees.

The outlook for Tuesday, according to the weather service, is cloudy, possible showers and temperatures in the 50s.