The global ensemble forecasts have backed off a bit from a prediction for heavy snow.
Basically, the storm that will bring the coldest air is forecast to move a bit east of its previously forecast position, reducing the time it spends over the eastern Mediterranean and our area.
There will be periods of rain and thunderstorm into Tuesday night, when the rain may mix with wet snow late Tuesday night and Wednesday morning in the central mountains, and peaks of the Galilee (snow in the Golan and Hermon).
Snow is likely sometime Thursday afternoon into early Friday morning. It looks like the arrival of the upper level "energy" (cold) will bring a burst of snow, which will probably make for dangerous driving in the area of the central mountains, and mountains of the Galilee.
Several centimeters of snow is possible, but there is still a lot of variability in the temperature and precipitation forecasts (several days in advance), so this is speculation (pending forecast information from our highest resolution model the day before).
The snow should end on Friday, regardless, but Shabbat will remain chilly.