No, it's just Harry's own nervous thoughts.
The only part that could be prophetic is the part about Quirrell's turban. The presence of Draco and Snape doesn't seem to connect with the events later in the year. Neither Draco nor Snape were working with Quirrell or Voldemort. Snape was a double agent and Draco, although he hated Harry, didn't have any real loyalty to Voldemort during his first year.
My guess as to why they were in the dream is because to Harry, they were the defining faces of Slytherin. He was terrified of being in Slytherin, and hated that the Sorting Hat considered putting him there, since he didn't want to be anything like the Slytherins he knew.
The Quirrell part is the only one that could possibly mean something. Harry wasn't afraid of Quirrell or anything he represents (Quirrell wasn't said to be in Slytherin and Harry had no reason to think he was any danger - he certainly didn't know Voldemort was attached to him) so had no reason to be dreaming about him or his turban. However, Harry is not a Seer, is never said to be capable of predicting the future, and has no history of having prophetic dreams.
But Harry does have a history of significant dreams - all having to do with the Horcrux inside him. The Horcrux could have been trying to convince him to join Voldemort. It wasn't particularly active until Voldemort regained his physical form, but it was present since Voldemort's first downfall when it attached itself to Harry.
Voldemort was hidden under Quirrell's turban, which could be why he took the form of Quirrell's turban in Harry's dream. Joining Slytherin could have been being used as an analogy for joining Voldemort, and Quirrell's turban saying that it's Harry's destiny could be the Horcrux trying to convince him that he was meant to join Slytherin and later Voldemort.
However, like the Dark Lord said in his answer, this particular dream doesn't really have any of the qualities of Harry's other Horcrux dreams, and it seems odd for a dream that has clear roots in Harry's own anxieties to be anything but a simple manifestation of Harry's fear.
The Dark Lord mentioned something that makes much more sense - it was his idea, I'm just adding it here so my answer follows better logic. The turban is a memorable type of headwear, just like the Sorting Hat, and the Sorting Hat was the origin of Harry's anxiety. He was nervous about the possibility of being in Slytherin and after the Hat told him he would be a good fit there, was nervous about what that meant about him.
The turban simply took the place of the Sorting Hat in Harry's dream, since it was another example of an odd hat that Harry saw during the day.
Out-of-universe, it's foreshadowing - meant to show Harry's fear and disgust with Slytherin, but also taking the opportunity to give a small hint to where the real danger lies and a nod to later events.