The Ringwriths were radiating horror and fear wherever they went, much like the Army of the Dead did; this seems to be inherent in their very nature, and was not due to any active action on their part ... and the fear was only temporary, passing away when the Nazgûl were no longer close by.
The Nazgûl could however also apply horror and fear actively on the minds of indivuals, in a power called the Shadow of Fear, which are not very well known, as it is only mentioned twice in the lore. This power apparently had a lasting effect, making the victim an agent for the Dark Lord:from Unfinished Tales, The Hunt for the Ring:
Sauron ... 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.
[...] Sauron did not underesteem the powers and vigilance of the Wise, and the Nazgûl were commanded to act as secretly as they could. ... The Lord of Morgul therefore led his companions over Anduin, unclad and unmounted, and invisible to eyes, and yet a terror to all living things that they passed near ... and rumour of darkness and a dread of men knew not what went before them.
... the Nine rode ever on into the North; and terror went before them and lingered behind them;
At length they returned; but the summer was now far waned, and the wrath and fear of Sauron was mounting. When they came back ... they met messengers from Barad-dûr conveying threats from their Master that filled even the Morgul-lord with dismay. ... Speed alone would now serve, and secrecy must be abandoned. ... They rode then through Rohan in haste, and the terror of their passing was so great that many folk fled from the land, and went wildly away north and west, believing that war out of the East was coming on the heels of the black horses.
This power is only mentioned in connection with Sauron and the Witchking, but as it was not exclusive to Sauron himself, we might assume that all the Nazgûl would be able to use it to some degree.from Unfinished Tales, The Hunt for the Ring:
Gollum was captured in Mordor in the year 3017 and taken to Barad-dûr, and there questioned and tormented. When he had learned what he could from him, Sauron released him and sent him forth again. He did not trust Gollum, for he divined something indomitable in him, which could not be overcome, even by the Shadow of Fear, except by destroying him.
This Dunlending was overtaken by several of the Black Riders as they approached the Tharbad crossing. In an extremity of terror he was haled to the Witch-king and questioned. ... The Witch-king had now a clearer understanding of the matter. He had known something of the country long ago, in his wars with the Dúnedain, and especially of the Tyrn Gothad of Cardolan, now the Barrow-downs, whose evil wights had been sent there by himself. Seeing that his Master suspected some move between the Shire and Rivendell, he saw also that Bree (the position of which he knew) would be an important point, at least for information. He put therefore the Shadow of Fear on the Dunlending, and sent him on to Bree as an agent. He was the squint-eyed southerner at the Inn.
