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 wimple is a cloth which covers the head and is worn around the neck and chin, worn by nuns in certain orders.
a hat
head
head-band
bandana
"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.
The Nemes which is a striped head-cloth worn by pharaohs in ancient Egypt.
Something you wear on your head like a hat.
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