What do you call the piece of clothing George Washington is wearing?

Solution 1:

For this sculpture, Horatio Greenough was inspired by The Statue of Zeus at Olympia that was a giant seated figure, about 13 m (43 ft) tall, made by the Greek sculptor Phidias around 435 BC at the sanctuary of Olympia.

The tunic worn by Zeus is a himation, a garment consisting of a rectangular piece of cloth thrown over the left shoulder and wrapped about the body. It seems that, for George Washington statue, the artist took some liberty by putting the garment on the right shoulder!

Statue

Marble statue of Zeus showing himation being worn. Dresden -Staatliche Kunstsammlungen, Skulptureensammlung 68.

Engraving from a work of Antoine Chrysostome Quatremère de Quincy (Le Jupiter olympien ou l'art de la sculpture antique).