Who makes that shrieking noise, the Nazgûl or the beasts they ride on?
Book 1, ch.4:
"A long-drawn wail came down the wind, like the cry of some evil and lonely creature. It rose and fell, and ended on a high piercing note. Even as they sat and stood, as if suddenly frozen, it was answered by another cry, fainter and further off, but no less chilling to the blood."
Book 1, ch.12:
"...and from the Riders came a terrible cry, such as Frodo had heard filling the woods with horror in the Eastfarthing far away."
Book 2, ch.1:
"‘Because they are real horses; just as the black robes are real robes that they wear to give shape to their nothingness when they have dealings with the living.’
‘Then why do these black horses endure such riders? All other animals are terrified when they draw near, even the elf-horse of Glorfindel..."
‘Because these horses are born and bred to the service of the Dark Lord in Mordor. Not all his servants and chattels are wraiths!"
It's the call of the Nazgûl themselves. They were riding normal horses up until they lost them at the Ford of Bruinen. The flying... things... don't show up 'til much later in the story.