Volume I, Book 4 of the Epic storyline deals with Rivendell trying to figure out what happened to the Nazgûl following the flood of waters as Frodo was pursued at the Ford of Bruinen. As I can't say often enough, if you are the sort to skip your Epic books, please go back and do them all!
Book 4 provides a nice creative opportunity for Tubrine to conjecture what became of one particular Nazgûl and his mount. While the fate is never discovered in the trilogy, the entirety of Book 4 is built on a very real excerpt from The Fellowship of the Ring.
Elrond then sends scouts out to various parts of Middle Earth, some to contact friends in other places, others to scour the land and gather what information they can before the party of the Ring sets forth. One piece of intelligence that is brought back has to do with the fate of the Nazgûl and their mounts:
"Three of the black horses had been found at once drowned in the flooded Ford. On the rocks of the rapids below it searchers discovered the bodies of five more, and also a long black cloak, slashed and tattered. Of the Black Riders no other trace was to be seen, and nowhere was their presence to be felt. It seemed that they had vanished from the North. 'Eight out of the Nine are accounted for at least,' said Gandlaf. 'It is rash to be too sure, yet I think that we may hope now that the Ringwraiths were scattered, and have been obliged to return as best they could to their Master in Mordor, empty and shapeless.' "
From this bit of Lore mystery - one missing mount, one found cloak - Turbine is able to weave a story about what just might have happened to that Nazgûl and his mount. Poor horsey. To learn that story, be sure to do Volume I, Book 4 or revisit it in a Reflecting Pool if it has been a long time.
Sources: The Fellowship of the Ring