I know. I've wondered sometimes... why did the Nazgûl need clothes so people would see them? Wouldn't it be to the Nazgûl's advantage that they were invisible?

As far as I know they wear cloaks when dealing with the living, to ask things etc.

I think as a second, their "weapon" is not invisibility, but fear. As for example in weathertop:

"Terror overcame Pippin and Merry, and they threw themselves flat on the ground. Sam shrank to Frodo's side. Frodo was hardly less terrified than his companions; he was quaking as if he was bitter cold..."

Here they used their fear instead of invisibility.

I think it is a way of strategy, using fear instead of invisibility.

Maybe also to do with that Sauron has some ignorance in believing that the ringbearer will use the ring instead of destroy it (As he finds out too late).

This last part is just what I think, as far as I know nothing was officially written down of this specifically.

Maybe.

@IAmCattima I have to agree with you on this. Sauron is a huge fool for giving the Nazgûls clothes. If they needed clothes to talk to people and find info on the hobbits then the Black Riders could have just gotten rid of their clothes and used some sneaky moves and steal the Ring.

Yeah.

@Jaccc0 said it. Their greatest weapon is fear. The black cloaks greatly enhance the fear factor.

Also, even when they're too far away to be seen (like flying overhead in the Two Towers) there's still a sense of fear and dread on everyone. So I don't think they would be able to necessarily surprise anyone even if they had no cloaks, because of the black breath and fear factor.