I'm guessing that Chrysaor covered his face because of three reasons:

* He was extremely ugly and disformed, so he hides his face in a mask. 
* Because he was paying tribute to his mother and rebelling against people.
* He could turn people to stone like his mother and so he wears the mask to make sure that he doesn't petrify his prisoners before slaying them.

Also, maybe he wants to leave a mark in the world, because he is not as recognized as his brother, Pegasus. So he decided to wear a golden mask to make sure that people recognized him. His name means "the golden one". Or something like that. I forgot the real meaning. But that is why I think that Chrysaor wears a golden mask. 

I've looked up why he wears a mask, but the resources are few and the ones I found are not very good. I'm just giving ideas on why he wears a mask. I'm a mythology nerd, and I know a lot about these things, so I gave my best answer.