They were painted!
Years of sun, salty air and just the passage of time have stripped the colors away, leaving the bare marble or bronze underneath.
(Here's another fun fact I discovered while double-checking my sources for this info: most Greek sculptures were actually bronze by the 5th century. Most of the marble ones we see today are actually Roman re-creations of the original bronze Greek ones -- which were susceptible to being melted down for use elsewhere when an invading army tromped through.)
But no matter what the base material used, it's clear that color was definitely applied on top. Even ancient Greek plays seem to confirm this, such as the line from the play "Helen" by Euripides (who lived from 480–406 BC):
For this … my beauty is to blame.
If only I were as hideous as a statue
from which the paint was wiped away,
The people would not have been subjected to such suffering.”
A little bright, isn't it? It's not what I expected either! Those early sculptures were made with flat color, but over the years, artists learned how to use shading and highlights to give everything a design that was a little more pleasing to the eye. Thank goodness!
[The bronze statue photo is from Wikipedia, while the image of the bright archer is from the Brinkmann's website, listed above.]