After one winter storm moved out of the Northeast on Thursday, leaving behind a glimmer of ice and snow and more than a few canceled school days, the next in line was smashing into the West Coast on Friday. By Saturday, it will have surged east, blanketing another strip of the Midwest and the Northeast with winter weather.

This is the second winter storm in a week to traverse the country, creating a dividing line of warmer rainy weather in the south and colder snowy weather to the north — and a messy wintry mix in between. Millions of people in cities like New York have been right along the dividing line, and with each storm that passes, a different combination of messy wintry precipitation may fall.

A dreamy snow may fall late on Saturday in New York City, but forecasters with the National Weather Service in New York cautioned that sleet or even freezing rain could nose into the city, especially in coastal areas, after midnight on Sunday.

Earlier on Saturday, the storm is expected to dump heavy snow from the Dakotas to the Great Lakes. Minneapolis, Des Moines and Chicago are all in the storm’s path, though any deviation north or south could change the type of precipitation that falls in those cities.

Small shifts could significantly affect where the heaviest snow falls, said Frank Pereira, a meteorologist with the National Weather Service. If warm air pushes farther north, cities like New York could see more sleet and freezing rain instead of heavy snow.

Cities including Buffalo, Albany and Boston are far enough north that they will most likely receive only snowfall. More than eight inches could accumulate across parts of Minnesota, New York State and New England by Sunday. Areas that are expected to reach more than eight inches of snow, and possibly as much as a foot, include upstate New York, northern Pennsylvania and New England, Mr. Pereira said.

Areas farther south, including Philadelphia and Washington, D.C., will most likely encounter sleet and freezing rain.

Looking ahead, forecasters are monitoring the potential for another wave of winter systems next week. Following almost a repeat pattern of the two winter storms this week, the next two storms could bring similar threats of more significant winter weather, including heavy snow, sleet and ice from the Ohio Valley to the Mid-Atlantic region, including Philadelphia, Baltimore and Washington.