In St. Louis, freezing rain is predicted to fall on top of a thin layer of snow, which will have "a significant impact on travel," the National Weather Service warned.

North of where the most snow will fall, Chicago could receive as much as 6 inches, CNN's Sarah Dillingham said. The city is running 15 inches below its average snowfall for the season.

Southern downpours

Severe thunderstorms moving in from the Gulf of Mexico are expected to bring 2 to 6 inches of rain to New Orleans and Montgomery, Alabama, according to CNN's weather center, before rolling up toward Atlanta.

The torrential rains could lead to significant river flooding, as flood watches are still in effect from last week's heavy rains.

Heavy winds, hail and tornadoes are possible, the National Weather Service said. Downpours are expected to continue into Friday.

Desert dwellers stunned

On Wednesday, the winter storm system left a rare thin layer of snow across the deserts of Arizona, New Mexico and southern California as far south as the border with Mexico.

"I've been here for over 10 years and I've never seen it snow like this," Kayla Avery of Tucson, Arizona, said in a CNN iReport, which came with a video of the snowfall.

"There is more snow on the ground in Tucson today than I have seen in over 30 years living here," Carrie Tucker said in another iReport.

Mona Jensen of Dolan Springs, Arizona, posted photos of her 8-acre property blanketed by snow.

Katie June in Yucca Valley, California, shared a shot of a snow-covered cactus.

"Some of the larger ones are having a hard time," she wrote. "But they all enjoy the drink!"

Joan Dedmon in Tuscon, Arizona, also found snow on cacti and shared a picture of a snow-covered birdfeeder. She said it confused the hummingbirds who were trying to get a meal before dark.