This question already has an answer here:
We all know Snape was a double agent (Death Eater and working with Dumbledore), but in the Sorcerer's Stone, he had no idea that Voldemort had latched himself onto Quirrell. This is evidenced in that that Snape is suspicious about some of the actions that he linked to Quirrell, and also confronts him about. But in the scenes that we see them talking privately, they never talk about Death Eater stuff.
I have not read the books and maybe there are talks of it in there, somewhere. But I think it would ruin the whole 'Snape is actually a good guy' plot line, so is that the only reason Voldemort did not expose himself to Snape?
Snape was also one of Voldemort's 'trusted' followers, because he let him get the teaching job at Hogwarts to spy on Voldemort (according to my sources).
It just did not make sense to me after looking a little into the Harry Potter series and re-watching the movies and this was the first thing that struck me as odd.
Why didn't Quirrell tell Snape about Voldemort?