According to the History of Fashion website, there were only a couple elements added to the dress of the Byzantine period. While togas had been popular, tunics replaced the wrapped clothing style and added long sleeves, which is assumed, though not not known, to be a reflection of a more Christian attitude requiring covering the body. Fabrics were also changed slightly. Instead of using simple fabrics, the Byzantines embroidered and beaded the fabrics. Essentially,the shape of the clothing of the period was still in keeping with Roman tunics and capes, except that, under short tunics, men wore trousers, a trend borrowed from Northern barbarians.
The Fashion Encyclopedia goes into more depth by providing the names of the garments worn by the Byzantine. Men's tunics were called dalmaticas; these long shirts were worn with a second layer of tunic. Women's tunics were called stola. Women wore their stolas with long undergarments and a cloak (paludamentum).
Although purple tended to be reserved for royals, all other colors were used in the dress of the Byzantines.