[Gurthang]

...especially ones as big as these. You could see them from miles away.

Another thought I've had was that, although the Wraith's steeds do die rather easily(too easily, in my opinion), having the Ring so near could have driven them to fight harder.

At the Black Gate the Eagles came upon the Ringwraiths in suprise, diving out of the sky and striking out almost before they were known to be there. The Ring's whereabouts were unknown. If the Eagles had Frodo and the Ring it would be different. First the Wraiths would see them coming, so no suprise attack. Second, with the Ring so close, they would push themselves and their steeds harder and fight more fiercely.

It seems to me that, if the Eagles did attempt this 'hit-and-fade', it would fail.