Is it permissible on Shabbat to wear a plastic covering on one’s hat to protect it from the rain while walking in a public area, or is this considered carrying on Shabbat?
A basic principle in Halacha establishes that something worn for the purpose of protecting a garment (known in Talmudic jargon as "Asuleh Tinuf") does not fall under the category of clothing with respect to the prohibition of carrying on Shabbat. Wearing such an article is therefore considered carrying, rather than wearing, and is forbidden in a public domain on Shabbat (except, of course, the area is enclosed by an acceptable Erub).
Seemingly, then, it would be forbidden to wear a hat covering in a public domain on Shabbat, since it is worn strictly for the purpose of protecting the hat, and not for comfort, warmth or fashion.
In truth, however, plastic coverings may be worn on Shabbat because they are worn as part of the hat. These coverings are specifically made to fit over the hat and be worn together with the hat, and they are therefore considered an accessory to the hat, rather than an extraneous article. It is thus permissible to wear a plastic hat covering on Shabbat in a public area without an Erub. One should not, however, go outside on Shabbat with an ordinary plastic bag wrapped over the hat. Since the bag is not made to fit on the hat, it cannot be considered part of the hat, and may therefore not be worn in a public domain without an Erub.
Summary: One may wear a plastic hat covering on his hat in a public domain on Shabbat, but one should not go into a public domain with an ordinary plastic bag wrapped over his hat.
