Flammifer,
1. The fact that the Nazgul no longer wear their Rings allows the cloaks to remain visible while their clothing and gear is invisible.
The clothing (robes of white and grey) that Frodo sees are then either really the memory of their clothes from ages past, regular clothing rendered invisible through contact with the invisible Nazgul, or long use of their Rings renders the clothing they were wearing for the long ages invisible with them (very hardwearing fabric if so).
2. The cloaks are specially treated to retain visibility while in contact with the invisible Nazgul, where regular items become invisible.
At Weathertop he could see 'beneath their black wrappings', while at the Ford of Bruinen 'He could see them clearly now; they appeared to have cast aside their hoods and black cloaks, and they were robed in white and grey. Swords were naked in their pale hands; helms were on their heads.'
So any supposition that the cloaks are 'holding them together' doesn't work, unless we lean heavily on the phrase 'appeared to'.
While folks are questioning the lack of boots being found, there has been no questioning to this point about the remainder of their gear (swords, helms, etc.)
I think this, combined with the very physical descriptions on the Pelennor suggest invisible corporeality is the default state for the Nazgul, and they would need to walk, not waft, back to Mordor. If the cloaks require special treatment to remain visible, that could explain why they simply couldn't raid clotheslines for new outerwear.
Both the 'wafting Nazgul' and 'walking Nazgul missing their specially treated cloaks' scenarios require a return to Mordor for re-cloaking, but one involves spiritual work, while the other requires special textile treatments. In either case, their travel is impeded by their poor vision.
The 'wafting' Nazgul should have left their boots, swords, and helms behind, and yet there is no evidence of this.
The 'walking' Nazgul can take them with them, albeit invisibly.
I like your logic Anthony.
One question. Do we know that the Nine are no longer wearing their Rings? From my recollection, the evidence on this is ambiguous?
If they are wearing their Rings, then the cloaks must have special treatment to prevent them from being rendered invisible.
If they are not wearing their Rings, then it stands to reason that the helms, swords, grey and white gaments, pale faces and hands, are the normal aspect of the Wraiths on the 'Other Side'. In this case, the cloaks could be normal cloaks, as there are no Rings being worn to make them invisible?
Now, if the bodies, visible on the 'Other Side' are mere illusions, and the Wraiths are truly incorporeal, then they could not sit on horses nor wear cloaks, nor could the Witch King 'spring forward' to attack Frodo with the Morgul Knife. He would have had to 'waft' forward.
So, we have two possibilities:
One is the 'supposition' - that the corporeal elements of the Wraiths, which allow them to sit on horses, wear cloaks, spring forward, etc. are special effects conferred on otherwise totally incorporeal beings by Sauron. In which case, why such elaboration? Why give them helms? crowns? garments of grey and white? swords? If the 'supposition' considers that Sauron weakens himself by conferring corporality powers on the Nazgul, why elaborate that corporality beyond what is needed to sit on horses, wear cloaks and speak?
Also, there is a question of timing. The Nazgul re-appear in Third Age 1300. In 1975, when the Witch King is defeated in the North, he is described as "black robed and black masked upon a black horse" (Appendix A). So, Sauron must have 'boosted' the Nazgul previously. However, Sauron is not suspected to have re-appeared in Dol Guldur until 2060. Under the 'supposition' was Sauron recovered enough to boost the Nazgul by 1300 or before 1975? If he 'boosted' them back in the Second Age, would that 'boost' have lasted through his death, weakening, and recovery?
The second possibility is that the Nazgul are always at least semi corporeal. No need for a 'boost' from Sauron. No need to 'waft' back to Mordor. In this supposition they are 'obliged' tactically, rather than spiritually, to return to their Master in Mordor, because they have lost mobility, they have become invisible, they are scattered, they cannot see well, they are near to scary Elves like Glorfindel and the other exiles in Rivendell, who can see them, they need to report and re-group.
Now, back to the question of whether or not the Wraiths are wearing their Rings? As far as I remember, the main passage which suggests that they do not wear their Rings is Galadriel saying,
"You saw the Eye of him that holds the Seven and the Nine", which people interpret as 'Sauron holds the Nine and the Ring-wraiths do not wear them'. But, Galadriel is clearly speaking metaphorically. We know that Sauron does not actually 'hold' the Seven. Gandalf already told us,
"Seven the Dwarf-kings possessed, but three he has recovered, and the others the dragons have consumed". So, Sauron does not actually 'hold' all the Seven, and might well not physically 'hold' the Nine. (Any other evidence about whether the Nine are with Sauron or with the Wraiths?)
If the Nine are wearing their Rings, it would offer an explanation as to why a black cloak was found at Weathertop. Quite simple. The Witch King, having stabbed Frodo with the Morgul Knife, and been rattled by the name of Elbereth, wanted to disappear. Drop the visible cloak, and poof he becomes invisible and heads off to await Hobbit wraithification.
(Another puzzle: At the approach to the Ford, Nine Riders are seen. The passage is all told from the view point of Frodo, but,
"to the dismay of Frodo and his friends out from the trees and rocks away on the left four other Riders came flying". If all Nine Riders were visible to Frodo's friends, how did the Witch King acquire another black cloak? Did he return to Weathertop, and retrieve the one that Aragorn found?
My speculation is that the Nine are wearing their Rings. That this renders them invisible. That the black cloaks are specially endowed so that they remain visible. That the Nine are only semi-wraithified, semi-corporeal. This seems to me a simpler explanation, with fewer knock-on problems, than the Sauron boost 'supposition'.