The northern counties of Kentucky near Cincinnati may get a brief burst of snow during the Friday-Saturday time period as the trough bringing the coldest of the arctic blast moves across the state. While this is not going to be an accumulating snowfall, the overall synoptic pattern is very similar to one of the last widespread April snows in Kentucky history.
April 18th, 1983 was last time measurable snowfall was recorded in many parts of south-central KY. Between 2-3 inches fell between Bowling Green, Mammoth Cave and Glasgow as a deep trough rotated through the eastern United States. Compare the pattern from the upcoming weekend with the 1000-500mb thickness, 500 mb heights, and the 850 mb temperatures from April 18, 1983.
The primary difference between the two cases is the lack of moisture in the mid-levels of the atmosphere for this upcoming weekend. During the April 18, 1983 snow, there was an area of 100% relative humidity over south-central KY during the first part of the day as a piece of short-wave energy swung through the base of the trough. For this weekend, you can see that there are no shortwaves, no moisture, no snowfall.