(REUTERS) - Snow continued to fall in the United States (US) South-west on Sunday in a storm system that may snarl Thanksgiving travel as it heads east, while biting Arctic winds plunged much of the East Coast to sub-freezing temperatures, the National Weather Service said.

Forecasters have warned that the winter storm now in the South-west could cause flight delays and icy roads for some of the millions of people travelling for Thursday's Thanksgiving holiday depending on the path it takes as it heads toward the East Coast.

"There's still a whole lot of uncertainty," Ms Lora Wilson, a National Weather Service meteorologist, said in an interview.

For now, the forecast was for heavy rain on Tuesday and Wednesday for much of the East Coast and Central Plains.

"If that's the case it will be your typical soggy-rainy-delay-type situation," she said, adding that skies will largely clear for Thanksgiving itself and the rest of the weekend.

The Thanksgiving holiday weekend is one of the most heavily travelled in the US.

Some 39 million people are expected to hit the roads from Wednesday to Sunday, centering around Thanksgiving Day, travel group AAA said earlier this week.

About 3 million people will fly to their destinations, according to AAA.

Up to 5cm of snow was predicted to fall in northern Texas and central Oklahoma on Sunday, the National Weather Service said. The storm has been linked to several fatal icy road accidents in Texas and New Mexico.

The storm is expected to bring heavy rain to the Southeast on Tuesday before heading north up the East Coast.

Meanwhile, an "Arctic airmass" was expected to chill much of the Central Plains and the East Coast through Monday, the advisory said, with wind-chill temperatures dropping into the single digits overnight in some places.

"These conditions would even be considered cold by January standards," the advisory said. "The only warm weather across the country will be in California, the lower elevations of Arizona, and Florida."