Purple skins in artistic depictions

Sure thing. I moved it to "History of South Asian Subcontinent" - is that OK?

My guess is it's a sex thing. Goddesses are often depicted with pink skin.

The blue-black tone can represent the night sky or infinity.  Krishna (an incarnation of Vishnu the preserver) is depicted with blue or black skin symbolizing his eternity.  The word Krishna itself is a synonym for "dark."

Shiva is also known as Nilkanth (blue-throated) and is sometimes represented in blue.  This goes back to the Hindu creation story where Shiva swallowed black poison churned up from the oceans, to prevent the destruction of the universe.   He is also often depicted in a grey hue as he is supposed to have covered himself in ashes during meditation. 

The goddess Kali is also depicted with blue or black skin.  She is the manifestation of vengeance and other dark emotions of the mother goddess. 

Well yes and no.  Only a few gods are depicted with bluish/black skins.  Most are depicted in more natural skin tones.