This is a very interesting subject, which I'd wondered about for a while, and more so over the last week or so. My opinion is that
Legolas was an
elf from the world of
elves. He had little understanding of the world from a mortal's perspective, which to me explains why he has no fear or dread (all of which are learned, IMO) of the
spirits of
men. Why should he fear them? His world of elves has no death unless a person is killed, and so ghosts of the dead are not a part of his world view. They likely don't have ghost stories, haunted houses, etc, so Legolas has no referrence point, and therefore no reason to fear ghosts.
The sons of
Elrond are (nearly) uniquely different. I believe they were elves, just as much (in quality, if not physical quantity) as Legolas. They had already been around for a long time before
Aragorn came on the scene, yet they were still his cousins and close companions. They had always known the
kings of men and their families (the
Dunedain). Elrond could actually be considered Aragorn's uncle, though a great-uncle many times over. Given that Elrond and his sons had always had their lives closely associated with the world of men, it's a good assumption that Elladan and Elrohir had a great deal of knowledge of ghosts, and things related to men and death.
Now whether they too had any kind of fear or dread of ghosts, to me it is uncertain. But I tend to think that they at least had some kind of apprehension before walking the paths of the dead, as did Aragorn. Yet still they went and followed it through to its end, as did he, putting aside any internal objections they had.
Also note that when telling
Merry and
Pippin about the experience, Legolas seems to have learned something new of ghosts. I'll quote it again:
"He fell silent; but Pippin and Merry were so eager for news that at last Legolas said; 'I will tell you enough for your peace; for I felt not the horror, and I feared not
the shadows of Men, powerless and frail as I deemed them.'
It seems to me that when he says that the ghosts of men held no fear for him, that he was speaking in the past tense. It appears that he now sees the spirits of the dead in a new light, and sees that they are more real than he had previously believed, and that they do have some kind of power. To me it's obvious that he's now hesitant to talk about it. Notice that instead of just telling them what happened, he goes silent. Then "at last" he talks about it. True, he "felt not the horror" when it was happening (when on the Path itself), but now he speaks in the past tense of "I feared them not", "I deemed them powerless and frail". Now, given all he's seen and experienced, he seems to think differently. So if they were all to walk along another Path of the Dead, Legolas would now think differently of it. As for Elrohir and Elladan, I think they'd had plenty of opportunity to learn of ghosts, both first hand and through the experiences of others. I tend to believe they had some kind of apprehension or dread before going with Aragorn on the Path of the Dead.