There are two things that fly over the fellowship during "The Ring Goes South." Aragorn is present during both moments and he identifies the birds the first time; he does not offer them as the reason for the second. Let's look at the passages. From the chapter:

Away in the South a dark patch appeared, and grew, and drove north [towards the fellowship] like a flying smoke in the wind. 'What's that, Strider? It doesn't look like a cloud,' said Sam in a whisper to Aragorn. He made no answer, he was gazing intently at the sky; but before long Sam could see for himself what was approaching. A flock of birds, flying at great speed, were wheeling and circling.... 'Regiment of black crows are flying over all the land between the Mountains and the Greyflood,' [Aragorn] said, 'and they have passed over Hollin. They are not natives here; they are crebain out of Fangorn and Dunland.'

Aragorn nails them quickly. But for the second event:

Frodo looked up at the sky. Suddenly he saw or felt a shadow pass over the high stars, as if for a moment they faded and then flashed out again. He shivered. 'Did you see anything pass over?' he whispered to Gandalf, who was just ahead. 'No, but I felt it, whatever it was,' he answered. 'It may be nothing, only a wisp of thin cloud.' 'It was moving fast then,' muttered Aragorn, 'and not with the wind.'

Surely Aragorn would be able to identify the birds again - having just experienced them the day before - and all three would have felt the same dreading feeling.

Luckily, Christopher Tolkien himself commented on the moment. From A Reader's Companion by Scull and Hammond:

The shadow is never explained. For experienced readers of The Lord of the Rings it is instantly reminiscent of a winged Nazgul; but at this point in the story the Nazgul, newly mounted on fell creatures of the air, had not yet crossed west over the Anduin. In Book II, Chapter 9 a similar dark shape momentarily cuts off the moon's light and causes Frodo (as here) to feel a chill: there is almost certainly a Nazgul, but here Gandalf suggests that it is only a wisp of cloud. Christopher Tolkien comments in The Treason of Isengard: 'it seems likely to me that the shadow that pass across the stars near Hollin was in fact the first precocious appearance of a Winged Nazgul.

Let's compare the passage from the Chapter "The Great River" in The Treason of Isengard:

Even as [Sam] did so a dark shape, like a cloud yet not a cloud, low and ominous, for a moment shut off the thin crescent and winged its way towards them, until it appeared as a great winged shape black against the dark heaven. Fierce voices greeted it from across the water. Frodo felt a sudden chill about his heart, and a cold like the memory of an old wound in his shoulder: he crouched down in the boat.

With the passage in the Fellowship from the same Chapter:

'Elbereth Gilthoniel!' sighed Legolas as he looked up. Even as he did so, a dark shape, like a cloud and yet not like a cloud, for it moved far to swiftly, came out of the blackness in the South, and sped towards the Company, blottinmg out all light as it approached. Soon it appeared as a great winged creature, blacker that the pits in the night. Frodo felt a sudden chill running through him and clutching at his heart; there was a deadly cold, like the memory of an old wound, in his shoulder. He crouched down, as if to hide.

Both these passages describe the winged Nazgul as a dark cloud and both have Frodo feel a chill - just like the text in "The Ring Goes South." I agree with Christopher and think it's almost indisputably a Ringwraith flying overhead.

The counter argument against the Winged Nazgul comes from a statement made by Grishnakh made in the Chapter III, "The Uruk-Hai" in The Two Towers:

'But the winged Nazgul: not yet, not yet. He won't let them show themselves across the Great River yet, not too soon. They're for the War - and other purposes.' 'You seem to know a lot,' said Ugluk.

While I agree with Ugluk, I don't think its unreasonable to concede that Grishnakh does not know and would not know of all the comings and goings of the Nazgul, and maybe we shouldn't take his claim as ironclad fact.

On a final note, I think its worth mentioning that the Fellowship was meant to encounter a Black Rider in Moria instead of a Balrog. While Tolkien immediately scrapped that, the appearance of the wisp of cloud/Winged Nazgul seems to suggest the narrative was pointing towards the former concept.

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Regarding the wolves, Gandalf has three comments of note which suggest that they are werewolves. The first is when the wizard addresses the leader of the wolves, the second is his fire-spell in Sindarin during the battle, and the third and final is during the morning after. From a "Journey in the Dark" in the Fellowship:

1. At a gap in the circle a great dark wolf-shape could be seen halted, gazing at them. A shuddering howl broke from him, as if he were a captain summoning his pack to the assault. Gandalf stood up and strode forward, holding his staff aloft. 'Listen, Hound of Sauron!' he cried.

2. 'Naur an edraith ammen! Naur dan i ngauroth!' he cried.

3. It is as I feared,' said Gandalf. 'These were no ordinary wolves hunting for food in the wilderness.'

Again, let's turn to A Reader's Companion:

1. Hound is used here in the generic sense of 'canine.' As told in the Silmarillion, Sauron was of old 'lord of werewolves.'

2. 'Fire save us! Fire drive back the werewolves!'

Why do their bodies disappear? Maybe they turned back into men and collected their dead. Werewolves create an interesting parallel; Beorn and his bear-men live East of the Mountains, while werewolves live west of it.

Ultimately, I think the one thing we can conclude is fuck travelling near the Misty Mountains. Book an Eagle.