It could be a Nazgûl, but probably not
The quote in the question is part of Glóin's report to the Council of Elrond on 25 October 3018 (Third Age). Glóin states that the messenger came to Erebor about a year ago, so that would be late 2017.
In Unfinished Tales, Tolkien describes the movements of the Nazgûl as they search for the Ring, but that account doesn't start until June 3018, several months after the messenger arrives at Erebor.
At length he resolved that no others would serve him in this case but his mightiest servants, the Ringwraiths, who had no will but his own, being each utterly subservient to the ring that had enslaved him, which Sauron held.
Now few could withstand even one of these fell creatures, and (as Sauron deemed) none could withstand them when gathered together under their terrible captain, the Lord of Morgul. Yet this weakness they had for Sauron's present purpose: so great was the terror that went with them (even invisible and unclad) that their coming forth might soon be perceived and their mission be guessed by the Wise.
So it was that Sauron prepared two strokes - in which many saw the beginnings of the War of the Ring. They were made together. The Orcs assailed the realm of Thranduil, with orders to recapture Gollum; and the Lord of Morgul was sent forth openly to battle against Gondor. These things were done towards the end of June 3018.
Unfinished Tales Part Three, Chapter IV, (i) Of the Journey of the Black Riders
Page 338 (Houghton Mifflin 1980 hardback edition)
There is no account of the whereabouts of the Nazgûl in the months before June 3018, so one of them could theoretically have been the messenger sent to Erebor.
However, the passage I quoted makes clear that Sauron was aware that the Nazgûl would be spotted when they traveled and carefully planned their appearance in June 3018. It seems unlikely that would have been necessary if one of them had already traveled to Erebor the previous year.
The passage also suggests that Sauron intended to use the Nazgûl only for tasks that they alone could accomplish. It seems unlikely that sending a message to Erebor was such a task.
So who was the messenger?
The bottom line, as far as I can see, is that the messenger was probably not a Nazgûl, but we can't completely rule it out. He could certainly have been an Easterling, but there is no particular evidence pointing in that direction (Sauron had many people under his control).