Snape is repeatedly referred to as a highly intelligent wizard, most skilled in the Dark Arts. We don't know for sure, but it seems probable he would know about Horcruxes, at least in theory.
He basically possesses all the same facts about the Harry-Voldemort connection as Dumbledore (that Harry can speak Parseltongue, that his mind is connected to Voldemort's etc), and about Riddle's diary: Dumbledore is not secretive about its origin at the end of Harry Potter and the Chamber of Secrets even with the Weasleys. While for Harry preserving a piece of someone's soul in a diary looks like a random act of magic, Snape would definitely recognize it as very peculiar case, same as Dumbledore did. Snape surely didn't know about Slughorn's memory, but he knew about Voldemort's ambitions in general as Voldemort stated himself at the end of Harry Potter and the Goblet of Fire:
"And then I ask myself, but how could they have believed I would not rise again? They, who knew the steps I took, long ago, to guard myself against mortal death?"
(Which to me sounds like Death Eaters could know about Horcruxes, but as Dumbledore keeps telling us they didn't, let's just believe him). Still it implies Snape knew the Dark Lord's final aim - immortality.
It seems out of character for Snape not to use his brains, put two and two together and get the same conclusions as Dumbledore came to.
Why, I'm even surprised Dumbledore himself didn't expect Snape to realize the truth.
UPD: Adding quotes that prove Snape didn't know about the Horcruxes (all from Snape's memories in the Deathly Hallows)
“He does not need protection. The Dark Lord has gone – ” “The Dark Lord will return, and Harry Potter will be in terrible danger when he does.”
Here we see Snape thinks Voldemort's gone for good, so he does not know about Horcruxes.
“Did you think that breaking the ring would break the curse?” “Something like that…I was delirious, no doubt…” said Dumbledore.
Here we see Dumbledore conceals the real reason he broke the stone. He doesn't want Snape to know it's a Horcruxe.
“What are you doing with Potter, all these evenings you are closeted together?” Snape asked abruptly.
Dumbledore looked weary...
"...I spend time with Harry because I have things to discuss with him, information I must give him before it is too late.”
“Information,” repeated Snape. “You trust him… you do not trust me.”
“It is not a question of trust. I have, as we both know, limited time. It is essential that I give the boy enough information for him to do what he needs to do.”
“And why may I not have the same information?”
“I prefer not to put all of my secrets in one basket, particularly not a basket that spends so much time dangling on the arm of Lord Voldemort.”
This does not require a comment I believe. Same as the next one:
!“But what must he do?”
“That is between Harry and me. Now listen closely, Severus... There will come a time when Lord Voldemort will seem to fear for the life of his snake.”
“For Nagini?” Snape looked astonished.
“Precisely. If there comes a time when Lord Voldemort stops sending that snake forth to do his bidding, but keeps it safe beside him under magical protection, then, I think, it will be safe to tell Harry.”
“Tell him what?”
Dumbledore took a deep breath and closed his eyes.
“Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself onto the only living soul left in that collapsed building. Part of Lord Voldemort lives inside Harry, and it is that which gives him the power of speech with snakes, and a connection with Lord Voldemort’s mind that he has never understood. And while that fragment of soul, unmissed by Voldemort, remains attached to and protected by Harry, Lord Voldemort cannot die.”
“So the boy…the boy must die?”
Nothing about Harry being a Horcrux, or Nagini being a Horcrux, or Voldemort having Horcruxes at all. Snape did not know and Dumbledore tried to phrase everything the way it would not specify the kind of magic.
UPD: here I found related topics that, though do not answer my question, may be interesting, so I leave the links here:
Why didn't any Death Eaters create their own horcruxes?