The National Weather Service in Birmingham has now added Tuscaloosa County to the current Winter Storm Warning. 

Tuscaloosa, Jefferson, and St. Clair Counties have been included in the warning area. You can read the full text of the warning below:

Tuscaloosa-Jefferson-St. Clair-
Including the cities of Tuscaloosa, Birmingham, Hoover,
Pell City, and Moody
630 AM CST Fri Dec 8 2017

...WINTER STORM WARNING IN EFFECT UNTIL MIDNIGHT CST TONIGHT...

* WHAT...Snow expected. Plan on difficult travel conditions,
  including during the morning commute. Total snow accumulations
  of 1 to 3 inches are expected, with the highest amounts on
  grassy and elevated surfaces.

* WHERE...Tuscaloosa, Jefferson and St. Clair Counties.

* WHEN...Until midnight CST tonight.

* ADDITIONAL DETAILS...Be prepared for significant reductions in
  visibility at times.

PRECAUTIONARY/PREPAREDNESS ACTIONS...

A Winter Storm Warning for snow means severe winter weather
conditions are occurring. If you must travel, keep an extra
flashlight, food and water in your vehicle in case of an
emergency.