Tolkien discusses that in the case of the ringwraiths, their bodies only have
become invisible, and without rings they are not able to turn their clothes and
personal items invisible. Suggesting that turning these things invisible is an
additional power of magic rings. (This from HISTORY OF MIDDLE EARTH, so perhaps
Tolkien's ideas changed before the final writing of LOTR.) I also get the idea
that if you learn to control a ring better you don't HAVE to turn invisible
when you wear one - like Gandalf, Galadriel,
Sauron.