In an early draft of this story, Gogol planned for the whole thing to be Kovalev's dream. Well, it seems like he went overboard in the rewrite, because he crammed realistic and specific details into every description as possible. Dreams are vague and strange and ambiguous, right? So what's less dreamlike than really getting in to the nitty-gritty aspect of everything?
And that goes double for the most dream-like element in the story—the nose itself. Every time we encounter it, we get drowned in details. The nose feels hard to the touch, it's got a zit on it on the left side, and when Kovalev finally sees it, we get such a long and complicated explanation of what it looks like and what it's doing that the nose ends up being the most described character in the whole story:
a door of the carriage opened, and there leapt thence, huddling himself up, a uniformed gentleman, and that uniformed gentleman ran headlong up the mansion's entrance-steps, and disappeared within. And oh, Kovalev's horror and astonishment to perceive that the gentleman was none other than—his own nose! […] It was clad in a gold-braided, high-collared uniform, buckskin breeches, and cockaded hat. And slung beside it there was a sword, and from the cockade on the hat it could be inferred that the Nose was purporting to pass for a State Councilor. It seemed now to be going to pay another visit somewhere. At all events it glanced about it, and then, shouting to the coachman, "Drive up here," reentered the vehicle, and set forth. (2.11)
We know exactly how it's dressed, even down to color and fabric. We know not just that it's moving around, but that it's moving like a guy who is in a big hurry (it "ran headlong," it "leapt"). We even know how it treats its underlings by the way it's not too angry but not too polite with the coachman. And none of the description is in any way surprised or concerned with the logistics of a nose doing any of these things. In fact, the way the info is laid out for us, it's easy to forget we're not talking about a person at all!
Like, how on earth can that thing be small enough to fit on Kovalev's face, but big enough to wear a State Councilor's outfit? And—we just have to ask—out of what part of its anatomy does it talk?