This particular one was in Chapter 21, "The Unknowable Room". Harry just learned from Dobby, with very little help from Kreacher, that Draco has been going to the 7th floor regularly, with a variety of other students. In a literal head-slapping moment, Harry realizes that the other students are just Crabbe and Goyle, who, with the help of polyjuice potion, look like first-year girls. So even though Harry knows he needs to persuade Slughorn to give him the real memory, he is obsessed with finding out what Draco is doing in the Room of Requirement. Hermione reminds Harry once again that he needs to concentrate on getting the memory from Slughorn for Dumbledore.
Harry didn't sleep well that night, thinking about what Draco might be doing in the ROR. Was Draco using it for a meeting place, a hideout, a storeroom, workshop? Well, he's at least close on the last two. But all that just led him to have a strange dream:
Harry's mind worked feverisly and his dreams, when he finally fell asleep, were broken and disturbed by images of Malfoy, who turned into Slughorn, who turned into Snape. . . [HBP-p. 456]
Now that's what really has me puzzled. Is Rowling connecting those three characters because our minds often do that sort of random connection in a dream, putting together pieces of our daytime thoughts and conversations, or is she using those three characters because there IS a connection between them?
1. There might be no particular connection or significance at all, except that in this chapter, Harry is thinking about these three characters--wondering what Draco is up to, trying to get the memory from Slughorn, and being irritated with Snape over his dementor essay.
2. Draco might be working with the help of Slughorn and Snape.
3. Draco, Slughorn and Snape are put together because each is concealing something from Harry (and from the reader).
4. Or. . .?
I'd welcome any comments on this one. I always seem to get stuck on Harry's enigmatic dreams.