Speaking of banding, that's another issue we could face. Snow banding is when you get a thin strips of heavy snow falling that look like bands due to winds coming together in these areas. These bands can produce snow accumulations even when temperatures are above freezing, just like in Jackson, Tennessee earlier this month when over an inch of snow accumulated with temperatures just above freezing.
Overall, I think areas in and close to Louisville can expect a dusting and maybe up to an inch of snow on grassy and elevated surfaces at some point tomorrow evening. If cooler air does not come in as quickly as expected this will remain a rain/snow mix or even just plain rain. Areas north and west of the Ohio River have the best shot for a light accumulating snow as they'll be slightly cooler and have an earlier switchover during the late morning hours. Most of the models are agreeing that we'll stay above freezing during most of this event, but we will be dipping down below that mark late Tuesday evening. This may create slick spots if any roads are wet from the snowfall during the afternoon. The 12z NAM (top left) is indeed the most aggressive on snowfall totals around here by looking at the snowfall output map, which you can see a larger view of by clicking. The 0z GFS (bottom left) is less aggressive, which is typical for it lately, and the Euro (which I cannot post here to copyright policies) keeps the snowfall along and north of the Ohio River. There are still a lot of small variables like exactly how fast the precipitation will move out of here and how much cold air will actually work into this process, so little details like these can drastically alter who gets snow and how much.