Radar is showing convective banding taking place. The NWS in Louisville has even reported thundersnow from one of these convective bands. This will create tight snowfall gradients that will mean places within the same county could have wildly different snowfall totals.
The SW-NE trending band of snow across western KY/TN will become more N-S oriented overnight as the storm becomes negatively tilted. I would also expect to see the most intense convective bands migrate towards the Bluegrass as the surface low intensifies. The radar also shows that the southern part of the snowfall band is becoming ragged as some drier air works in. This could limit snowfall totals in the Nashville region and even Bowling Green.
I have no changes to my forecast of 1-3″ overnight for Bowling Green. As before, I will retain the caveat that if a convective band does set up over Bowling Green for any extended period, snowfall totals could be much higher.