Radar at 4:07 pm shows some light to moderate precipitation driving down I-24 from W Kentucky and S Illinois:
Wx models keep that precip coming. Almost all precip today has fallen as snow flurries, which should continue tonight. The HRRR thinks we’ll be up to an inch of accumulated snowfall as of 4am Tuesday morning. Keep in mind, this is just one weather model, not a forecast, and could be wrong:

But, will it stick? The NWS think it might, mostly in Davidson County:
MUCH OF NORTHEASTERN MIDDLE TENNESSEE HAS SEEN TEMPERATURES REMAIN AT OR BELOW THE FREEZING MARK THROUGHOUT THE DAY AND BELIEVE HAZARDOUS DRIVING CONDITIONS WILL QUICKLY DEVELOP OVERNIGHT, ESPECIALLY ALONG UNTREATED ROADWAYS, BRIDGES AND OVERPASSES, AS THE SNOW INTENSITY INCREASES. SOME SLIPPERY SPOTS COULD ALSO DEVELOP ALONG ROADS IN OTHER PARTS OF THE MID-STATE, ESPECIALLY NORTH AND EAST OF THE I-24 CORRIDOR (INCLUDING THE NASHVILLE METRO AREA). EXPECT UP TO AN INCH OF SNOW IN AREAS JUST WEST OF THE CUMBERLAND PLATEAU, RANGING TO AROUND ONE HALF INCH IN THE NASHVILLE METRO AREA.