Winter in the northern area of Israel is a mild affair, with rainfall rather than snow. Rainfall during an Israeli winter is sporadic but heavy, making some sort of rain gear and waterproof footwear advisable, as well as a light jacket for extra warmth. This will be all you'll really need to handle the winter in northern Israel, as the average temperature in this area during winter falls between 40 and 65 degrees.
The southern area of Israel is where the Negrev Desert lies, which would make it seem as though a winter season here would be nonexistent. In truth, while the southern region of Israel is hot and dry most months of the year, the Negrev Desert region can experience fairly heavy rainfalls of short duration in the winter, again making rain gear advisable. Nights can be surprisingly cool in this hotter region of Israel, but temperatures here don't fall enough to produce snow. Wool coats, hats, and scarves aren't necessary. Umbrellas, slickers, and galoshes are the recommended clothing for a winter in Southern Israel.
The West Bank area of Samaria and Judea is hill country, with land elevations of 1,600 feet to 3,500 feet. During winter months, rainfall may be heavier here than in the north, and light snow has been known to infrequently fall on the higher elevations. Those familiar with brutal, blizzard conditions in winter will find any snowfall in the hill regions of Israel to be mild in comparison. A light wool coat, scarf and gloves will suffice during the very occasional snowfall, and will most likely not need to be worn nearly as much as rain gear and a light jacket.