there are two ways to do the guitar effect that makes it sound like a horse wailing.
One way to do it is to do a pinch harmonic (place your thumb on the pick so immediately after you pick the string, your thumb will lightly touch the string) on an un-wrapped string (G, B or e) then bend it very high and slowly release the bend and as your releasing, vibrato with the whammy bar
Another way to do it, which I think sounds much better, is to do a natural harmonic (quickly, lightly touch the string with your fretting hand) near the 2nd fret of the G string, then on the whammy bar, go down, then pull up and vibrato with the whammy bar and as your vibrating, go down on the whammy bar.
For full lessons on how to perform harmonics, click here
[To hear the horse sound effect, listen to the song from below and the first time its used is at about 1:12 into the song.]