It could be a wig, hat, headscarf, helmet, woollen hat, etc. Personally, I wear a woollen hat when it is cold.
These are skullcaps, so they are worn over the head.
A chador (SHa-DOR) is worn over the head.
a hat
A wimple is a cloth which covers the head and is worn around the neck and chin, worn by nuns in certain orders.
head
bandana
head-band
The Nemes which is a striped head-cloth worn by pharaohs in ancient Egypt.
Something you wear on your head like a hat.
"Tefilin" (see a dictionary). One worn on the head, another worn on the arm, during morning prayer,every day except Sabbath and holidays, beginningat Bar Mitzvah.
shawls, stoles, capes, serapes and ponchos are or can be worn over the shoulders. Shawls can also be worn over the head and shoulders.
bubble wrap your head