The snow target time is Friday morning.
The below NWS Nashville graf has good information for Middle Tennessee:

Takeaways for us in Davidson and Williamson Counties:
National Blend of Models predicts 2″ of rain this weekend.
BEST GUESS TIMING. Most likely start time between 6 PM to midnight Saturday night. Ending around lunch Sunday. It’s possible rain could arrive as early as noon Saturday and end earlier Sunday morning -or- start later Saturday night and linger into Sunday afternoon.
Rain showers later today/tonight.
Near/Freezing Morning Temps & Thursday’s Marginal Fire Danger
Big Rainmaker Coming This Weekend
Quick References:
Weather changes constantly.
Follow @NashSevereWx on Twitter for any changes to this forecast.
Skies clearing today. Looks pretty good.
2. Tuesday morning. Cold brief rain if the HRRR is right (model cuts off before arrival):
3. Weekend rain. Timing and “accuracy” iffy at this range. A soaker is best bet. Not sure if Saturday or Sunday or both. May involve thunderstorms but no current severe concerns. Notice those pinks and blues as the system moves away – common false flag for wintry precip. More about this system tomorrow.