what causes rattleand vibration when starting car in cold weather?

I would suspect the dampness is causing a break down in the ignition and is causing a misfire but that should trigger a Check Engine/Service Engine Soon Light to come on. Secondly it could be an exhaust heat shield that is causing a rattle, as the metal expands with heat the noise may go away. Hard to guess without being able to hear the noise.

no idea, but mine does it without the vibration, then goes away when i put it in drive and pull away. Does not seem to be a serious problem.