Mr. Neigh-Neigh, also spelled Mr. Nay-Nay, is Big Daddy's fluffy pink horse pillow. Big Daddy hid it under his blankets in his bed. Whenever he woke up from a nightmare, he'd cuddle with it, but in secret. He made his first and only appearance in Big Wanda.
When Mama Cosma kidnapped Big Daddy, Cosmo was devastated by the loss of Mr. Nay-Nay and only joined the search for Big Daddy to post "Have you seen this pillow?" posters all over Fairy World. When Big Daddy was eventually found, Cosmo was overjoyed to see Mr. Nay-Nay again. ("Mr. Nay-Nay's so happy, he's ticking with glee!") But Mama Cosma had placed a bomb inside him in an attempt to blow up Wanda. Big Daddy throws it away just in time and Mr. Nay-Nay explodes into fireworks above their heads.
He is a fluffy pink horse pillow that has purple hair and blue eyes.
Cosmo treats Mr. Neigh-Neigh like an actual person.
He is actually a reference to the Decapitated Horse Head in The Godfather.
This also makes sense since the horse head was seen in Mr. Woltz's Bed, and Mr. Neigh Neigh the pillow is just a horse head and pillows are used for sleeping.
The bomb placed by Mama Cosma is another Godfather reference, as the bodyguard of Michael.