"The snowfall will not be as heavy as in some of the recent storms we have had, but it's going to be pretty far-reaching," said Weather Channel principal forecaster Roy Lucksinger.
Read MoreEast Coast refineries seize up with deep freeze
"It is already affecting the southwestern U.S. and the Rockies and will affect pretty much the entire nation before it moves out of the picture on Thursday, so from a geographic perspective it is a pretty large storm if not quite as potent as some of the others."
He said cold air meant precipitation from the storm would switch "back and forth from snow to rain and back again" in some areas, such as the Ohio and Tennessee valleys, with an icy mix possible from the southern Plains, including Dallas, into parts of the Southeast.
Snowfall may become locally heavy for parts of the Ohio Valley on Wednesday night — up to 10 inches or so. As the colder air reaches the Northeast on Wednesday night, light to moderate snowfall is expected from power-pummeled Boston down to Washington, D.C.
Read MoreMore icy mess ahead
Meanwhile, increasingly warm and moist air was set to trigger showers and thunderstorms across the Southern on Tuesday through Thursday. Locally heavy rain may cause some localized flooding in spots, especially in snow-packed areas of Kentucky, the Weather Channel said.