The latest forecasts from the GEFS (Global Ensemble) indicate that the upcoming storm will most most likely not produce any accumulating snow in the Jerusalem area.
The basic "problem" is that the area of coldest air is forecast to slide just to the north and east of Israel Thursday night, meaning that precipitation will be lighter than thought originally, and the chance for snow particles to grow large is quite low.
However, winds will gust to gale force levels, and rain amounts will still be on the heavy side, so at least there should be more rain to add to our already (what was) normal totals. Rainfall amounts should be heaviest up north.
Looking ahead: next week looks to be stormy, and we'll keep in mind that cold air may be arriving from the north. In such a situation, the longwave pattern is more greatly amplified (called an "Omega" pattern after the Greek letter Omega). This means that the lower level air is more likely to remain cold and that the stormy weather could possibly remain pretty much all week long.