This started several months ago. I can feel it in steering wheel & gas pedal. I thought it was the tires so I put 2 new tires on front, but no change.Tires had no unusual wear. Happens at any speed, worse around curves, left or right. Worse when temp is colder, 55 degrees, better at 75 degrees. Not affected by braking or in coasting neutral. No problem with steering or pulling.
Try swapping the new front tires with the old rear tires and see if anything changes.
Also, how many miles does the Cobalt have on it?
Have you kept up all the recommended maintenance?
Does it vibrate when stopped or only when rolling?
Any other symptoms? CEL light?
Any recent repairs? Recent accidents?
Inspecting your car remotely via the internet where the rotating parts and suspension can not be seen for an apparently obscure problem such as this may be impossible.
Loose steering component?
Brake rotor or drum problem?