Patchy rain, drizzle, and fog are all possible overnight and early Wednesday morning. The morning commute may require a bit more time if the expected visibility issues are down near zero.
Periods of rain and drizzle should play out Wednesday. But unlike Monday and Tuesday, I don't see periods of blanket rain coverage; spotty is a good descriptor.
Thursday afternoon should see some clearing of the sky. Colder air should start arriving Thursday night.
By Friday morning, the winter chill will be felt. Expect cold to, more or less, be our norm through the end of the month and most of February; at least models suggest for now.