A significant winter storm was settling into portions of the Mid-Atlantic and the Northeast on Sunday before dangerously low temperatures envelop much of the country in some of the coldest weather in years, National Weather Service forecasters said.

Snow started in the Appalachians on Sunday morning, and was falling in parts of the Mid-Atlantic, including New York City, in the afternoon. The heaviest snowfall is expected north and west of the Interstate 95 corridor, with up to eight inches possible, according to the Weather Service.

Areas from northern Maryland to Boston could get three to six inches of snow, with some spots potentially getting more. Northern Virginia to southern New Jersey may get a mix of rain and snow.

Much of the Northeast is under winter storm warnings or winter weather advisories. A winter storm warning is issued when severe winter weather is expected or already occurring, and could make travel extremely dangerous or even impossible. An advisory is for less severe conditions.

The New York City metropolitan area, Long Island, southern Westchester and coastal Connecticut are under winter weather advisories until 4 a.m. on Monday. Snowfall accumulations of three to five inches are expected, which may lead to slippery travel and snow-covered roads through Sunday afternoon and night.

Ground stops were possible and delays were expected later in the day at airports in the Northeast, according to the Federal Aviation Administration.

The affected airports included the four major airports in the New York metropolitan area, Dulles International Airport and Ronald Reagan Washington National Airport near Washington, D.C., as well as at Baltimore/Washington International Thurgood Marshall and Philadelphia International Airports. Delays were also expected at Boston’s Logan International Airport, according to the airport’s website.

Airlines, including Delta, American and JetBlue, said they would waive fees for some ticket changes made by affected travelers.

Forecasters at the New York office of the Weather Service warned that snowfall rates could be up to one inch per hour at times. Inland areas of New York, such as the Lower Hudson Valley, may get up to eight inches of snow.

Immediately after the storm clears out early on Monday, arctic air will plunge across most of the south-central and southeastern parts of the United States, bringing several days of frigid conditions.

This is the coldest air of the winter season so far, and in many cases the coldest in several years, forecasters from the National Weather Service warned.

The high temperatures will be from below zero to single digits in the Northern Plains and the Upper Midwest; single digits and teens across the Rockies, the central Plains and the Midwest; the teens and 20s across the Northeast and the Mid-Atlantic; and between the 20s and 30s in Texas and the Southeast.

The Weather Service said wind chills would be at dangerously low levels and hypothermia or frostbite could occur with prolonged exposure or lack of proper clothing.

Wind chills from 30 to 55 degrees below zero are expected at times on Monday in the Rockies, the northern Plains and the Upper Midwest, and subzero as far south as Oklahoma and the Tennessee and Ohio Valleys.

In Chicago on Sunday, temperatures were in the single digits at 11 a.m.

Ann Marie Saviano, 51, who lives in the Garfield Ridge neighborhood on the city’s South Side, said she had plans to meet friends for brunch, go grocery shopping and attend a birthday party.

“It’s that time of year we call hibernation season — when people retreat into their dens to stay warm and cozy for one to four days, and emerge ready to face the world when it’s a balmy 23 degrees,” Ms. Saviano said.

“But this is Chicago,” she added, and people still have to get things done.

Cheryl Atwood, 50, from Chicago’s Lincoln Square neighborhood, was buying groceries on Sunday and said she had a full day planned on Monday. “Everyone I know, it’s business as usual,” she said.

Forecasters warned of a significant winter storm across the Gulf Coast states coming Monday, as a combination of frigid air and a storm system over the Gulf is expected to bring snow, freezing rain and ice to the region that could lead to major travel disruptions.

As the storm moves eastward from Texas, it is forecast to sweep across Alabama, Georgia, Louisiana, Mississippi and the Carolinas.

The National Weather Service has issued winter storm watches for portions of Louisiana. The most snowfall is likely to be between the U.S. 190 and Interstate 10 corridors of Louisiana and southeast Texas, where four to six inches may accumulate. Farther north and south of this, three to four inches are expected.

By Tuesday night, the storm is expected to reach the Atlantic coast, bringing icy or wintry weather farther north.

Amanda Holpuch, Camille Baker and Robert Chiarito contributed reporting.