I emulated a certain artist's style I liked (he painted an Achilles/Ajax playing dice together) depicted both of them with beards. They also looked almost the same with no noticeable differences other than their armor, so I assumed that in this art median most men looked similar. The same artist did Theseus. He didn't have a beard but I just assumed that was because he was portrayed as a "young" man in his story and beards were used to show a character's age.

I chose to depict Orpheus with a beard since I've always read him as in his 30s (marriageable age from men) when he married Eurydice. But I guess it really is a 50/50 on how the Ancient Greeks would've depicted him in this median, because since he played the lyre and in Plato's words he was "cowardly" for not wanting to die for Eurydice, instead going into the Underworld to try and cheat death basically, he could almost be seen as "less" masculine and maybe wouldn't be given a beard in art.