May one place a plastic hat rain cover on a hat or Sheitel on Shabbos?
It is permitted to put on a rain cover onto one’s hat on Shabbos and doing so does not pose an Ohel prohibition. This applies whether the cover is special manufactured hat rain cover or one is using a plastic bag. The following will discuss if one may walk with this hat cover in an area without an Eiruv:
Area without Eiruv-Hats: Some Poskim rule it is forbidden to wear a rain cover for a hat in an area without an Eiruv even if the rain cover is manufactured for this purpose. Other Poskim rule it is permitted to wear a rain cover that is manufactured for hats even if one will be walking in an area without an Eiruv. Practically, even those that are lenient are only to do so with a manufactured hat rain cover and not through placing a plastic bag over the hat, in an area without an Eiruv. Those who are careful not to carry even in an area with an Eiruv may be lenient in this regard to wear a hat rain cover.
Area without Eiruv-Sheitel: Sheitel rain coverings that cover the entire head, as well as the ears and part of the face for protection from rain or warmth, are not subject to the above debate in Poskim and may be worn freely on Shabbos, even in an area without an Eiruv. However, those coverings that only cover the actual Sheitel and are worn to protect the Sheitel from rain, are subject to the same debate mentioned above regarding wearing hat rain coverings in an area without an Eiruv.
 The reason: As the Ohel prohibition does not apply in a case that there is not a Tefach of space between the cover and the hat. [Admur 315/19; 315/12; 640/10; Michaber 315/13; Rambam 22/23] B) A hovering made to protect an item [in contrast to a human] does not have the status of an Ohel when covering an item less than the size of a barrel. [See Admur 315/19 regarding a barrel]
 Piskeiy Teshuvos 301/6 [old] 301/20 [new]
 Minchas Yitzchak 3/26; Igros Moshe 1/108-110; Mahariy Shteif 73 and 124; Dvar Yehoshua 2/129; Betzel Hachochmah 2/80; Or Letziyon 2/23-3; Poskim in Piskeiy Teshuvos ibid footnote 144
 The reason: As a clothing worn to protect from rain falling on another clothing is not considered a clothing unless it covers majority of the body, and one hence transgresses carrying an item on Shabbos even when worn. [See Admur 301/11] It is unlike the allowance brought in Admur 301/11 and 43 which allows wearing one hat on top of another due to the rain, as that case refers to a hat that is wearable during the week even not during rain and is thus considered a clothing in its own right. However the rain hat is unwearable during non-rain times, and is hence not considered Derech Malbush. It is rather similar to one who wears a cloth over his head to protect his scarf from rain in which case we rule it is considered a Masuiy, as it is not Derech Malbush. [See Admur 301/11 and 43]
 Chelkas Yaakov 1/99; Har Tzevi 1 Tal Harim Motzi 2; Shevet Halevi 1/61; Divrei Yatziv 1/147; Cheshev Haeifod 1/81 and 2/67; Beir Moshe 2/31; Az Nidbaru 1/71; 4/37; Bris Olam Motzi 10; Tzitz Eliezer 10/23; Tiferes Adam 2/11; SSH”K 18/10 in name of Rav SZ”A regarding Karmalis; Mishneh Halachos 2/72; 6/72; Yabia Omer 5/24; 9/108-146; Poskim in Piskeiy Teshuvos ibid footnote 145
 The reason: As one may wear one hat on top of another on Shabbos even simply to protect from rain [Admur 301/11 and 43] and this hat cover is considered a clothing being that it is made to the same fit as a hat and is worn as a Derech Malbush. [Shevet Halevi and Poskim ibid] Likewise, it is also worn to protect the person from rain, in which case we rule one may cover the hat even if it is not a true clothing being that it is worn as a Derech Malbush. [See Admur 301/11]
 Piskeiy Teshuvos ibid; See Piskeiy Teshuvos ibid footnote 148 for Poskim who are lenient even in such a case
The reason: As no one walks outside with a plastic bag covering them, and hence it is not considreed a Mlabush even when used as such. [See Admur 301/43]
 Piskeiy Teshuvos ibid footnote 147
 See Admur 301/11; Avodas Hagershuni 80 [1600’s]; Minchas Yitzchak 3/26; Betzel Hachochmah 2/80; Beir Moshe 6/120; Piskeiy Teshuvos 301/20 [new]
 The reason: If it covers the ears and the like it is considered a regular clothing and is unlike the case mentioned in Admur 301/11 that prohibits wearing a clothing to protect from rain unless it covers majority of the body, as that is referring to when the entire intent is to protect the head clothing from rain, however when one also intends to protect oneself from the rain then it is permitted even if it does not cover majority of the body, as explicitly written in Admur ibid.