COLUMBIA, Mo. — A monster winter storm took aim at a third of the nation Monday, threatening to lay a potentially deadly path of heavy snow and ice from the Rockies to New England, followed by a wave of bitter, bone-rattling cold that could affect tens of millions of people.

Cities including St. Louis, Kansas City and Milwaukee could be hardest hit, with expected midweek snowfalls of up to 2 feet and drifts piled 5 to 10 feet. Even hardy Chicago could be in for whiteout conditions.

“I wouldn’t want to be on the road in open areas tomorrow night,” said forecaster Tom Skilling of Chicago television station WGN. “I don’t think I’d want to be driving in the city either. The fact is people die in these things. They skid off the road and go wandering around in whiteout conditions.”

Warmer areas were not safe, either. The system could spawn tornadoes in parts of the South.

While record snowfalls have pounded the Northeast in one of that region’s most brutal winters, the Midwest has been comparatively unscathed, until now.

A blizzard watch was in effect for today and Wednesday for southern Wisconsin, northern Illinois and northwest Indiana. Winds could reach up to 60 mph in open areas and near Lake Michigan.

In St. Louis and much of Missouri, residents braced for a particularly hazardous mix: up to an inch of ice, followed by 3 to 4 inches of sleet, then perhaps a half-foot of snow or more. To the west in Columbia, Mo., forecasters predicted between 12 inches and 16 inches of snow, prompting the University of Missouri to cancel classes through Tuesday night.

In Chicago, forecasters predicted 20 inches of snow.

Even when the snow stops falling, the temperature will keep dropping.

Bitterly cold temperatures were forecast in the wake of the storm, with wind chills as cold as 40 degrees below zero possible in parts of the Dakotas.

In Arkansas, most communities expected lesser amounts of snow, but the weather service warned of severe thunderstorms that could generate hail and isolated tornadoes.

After burying the Midwest, the storm was expected to sweep into the Northeast, parts of which already are on track for record snowfall this winter.