[Marileangorifurnimaluim]

No, they were not dead

It seems there were three planes
1) the physical
2) the unseen, the consciousness, metaphysical body
3) the mortal shades

The living had both the physical body and and the unseen. Note, Glorfindel appeared simultaneously in both the seen and the unseen, as did the others at the Fords, although shadowy - and fire appeared, too! Also, it's stated throughout the LotR that Sauron could not 'Make' something that didn't already exist, so the rings had to be working with something that existed already.

The Nazgul only had the second, the Unseen body. Their physical bodies had faded; but their will, volition, consciousness (even their personalities) and ability to effect the world remained. They could still slay, ride horses and so forth. Galadriel's description to Frodo of what he would need to use the ring - strength of will - supports the idea that will and consciousness are bound up in the use of the rings. The fact the Witch King of Angmar was Sauron's Captain at Minas Tirith indicates they are alert to the present and able to make decisions.

The mortal dead had no such volition, did not continue, couldn't hold conversations with their dead friends, write poetry, or effect the physical world. They continued only by the force of what unfinished business held them to life, could not create new ideas, dream new dreams. Or effect the physical save with fear.

This has a couple interesting implications:
- In ME the Unseen consciousness has form
- It is not dependent on physical form
- The Unseen gives a truer (or deeper) picture of the essence of a being, seeing Glorfindel "an elf lord revealed in his wrath" and seeing Galadriels motives.