Not really. Women sometimes pulled up their palla (which is a garment sort of like a scarf or a shawl) over their heads, and the Phrygians wore a cap that was sort of like a Smurf hat, but it wasn't really worn outside of the Phrygia and then there was a cap that was called a pileus which was symbolic of freedom and given to slaves when they were freed (Ancient Greeks wore that hat too, but it lacked the same symbolism) and then, of course, the helmets of soldiers and laurel wreaths.