Like so much of their costume tradition, the Byzantines inherited their basic hairstyles and forms of headwear from the Romans who preceded them in ruling the Mediterranean world. Men tended to wear their hair short and cut straight across the forehead in what is today known as the Caesar cut, named after the Roman general and statesman Julius Caesar (100–44 B.C.E. ). Women wore their hair quite long and tended to braid or pile it on top of their head in a variety of different fashions. They might use pins or a ribbon to hold their hair in place. There wasn't one typical Byzantine hairstyle for women, but instead a variety of ways of curling, twisting, and molding hair in pleasing ways.
Byzantines did not have a strong preference for specific forms of headwear, though there are several hats and crowns that appear to have been in use. Several hats inherited from the Greeks were worn, including the Phrygian cap and the petasos. Both male and female members of the Byzantine court, including the emperor, did wear a variety of crowns, usually heavily laden with jewels. Perhaps the most distinctive headwear worn in the Byzantine era was that worn by members of the Christian clergy. Clergymen often wore a round skullcap called a zucchetto, with the color depending upon whether they were a bishop, a cardinal, or a monk. A similar hat is worn by notable figures in the Roman Catholic Church to this day, with the pope's white zucchetto being the most famous example. Finally, monks might wear a kind of paludamentum, or cloak, with a hood pulled up over their head to keep them warm.
Cosgrave, Bronwyn. The Complete History of Costume and Fashion: From Ancient Egypt to the Present Day. New York: Checkmark Books, 2000.
Houston, Mary G. Ancient Greek, Roman, and Byzantine Costume and Decoration. Lanham, MD: Barnes and Noble, 1977.