The Great Eagle Mystery

[Raynor]

I might be wrong, but there's nothing in the book to say that Sauron could not go there and ruin the party for the eagles.

In letter #246, Tolkien states that:

Sauron should be thought of as very terrible. The form that he took was that of a man of more than human stature, but not gigantic. In his earlier incarnation he was able to veil his power (as Gandalf did) and could appear as a commanding figure of great strength of body and supremely royal demeanour and countenance.

In the same letter, he comments on how Sauron himself would come to claim the ring from Frodo (if he didn't destroy it). In The black gate opens, TTT, Gollum says that "he has only four (fingers) on the Black Hand", which is a further indication that Sauron has a body.