CHICAGO (CBS) — Chicagoland woke up to some pretty brisk wind chills on Tuesday morning and much of the area can now expect a bit more snow soon.

Over in southwest Michigan, there is a winter weather warning for lake effect snow. Portions of northwest Indiana were also experiencing snow Tuesday.

Starting Wednesday night and into Thursday morning, a quick-moving system will sweep the area, with an additional inch or two of snow possible.  A bit more lake effect snow is likely.

On Monday, the northern suburbs had two to three inches of snow, with trace amounts around the city and western and south suburbs.

The Emanuel Administration Tuesday declared Chicago “ready” for winter, with equipment, personnel and salt in place.

“We have more than enough salt for the city to handle this entire this winter — and more. But more than just the material, the trucks, the individuals that are ready to drive that truck any time of night, day, in the wee hours of the morning. We also have the leadership that’s ready,” Mayor Rahm Emanuel said.

By the weekend, the forecast calls for temperatures in the 40s.