Scraps had to climb over the fence to approach the Woozy about its three hairs. What she discovered was a very curious creature, indeed!
The creature was all squares and flat surfaces and edges. Its head was an exact square, like one of the building-blocks a child plays with; therefore it had no ears, but heard sounds through two openings in the upper corners. Its nose, being in the center of a square surface, was flat, while the mouth was formed by the opening of the lower edge of the block. The body of the Woozy was much larger than its head, but was likewise block-shaped—being twice as long as it was wide and high. The tail was square and stubby and perfectly straight, and the four legs were made in the same way, each being four-sided. The animal was covered with a thick, smooth skin and had no hair at all except at the extreme end of its tail, where there grew exactly three stiff, stubby hairs. The beast was dark blue in color and his face was not fierce nor ferocious in expression, but rather good-humored and droll.
Scraps got him out by having him burn down the fence, following his suggestion to say "Krizzle Kroo!" which made him very angry because he didn't know what it meant. In exchange for this, he decided to let them have his three hairs, even though they were his only hairs and he considered them his prettiest feature. However, they were impossible to be pulled out by hand. So, Ojo had to take the Woozy along.
The Woozy was very square (fair and reasonable in demeanor). Since Ojo had a replenishing stock of bread and cheese, he gladly shared it with the Woozy, and when Ozma made him part of the curious menagerie in the Palace, Dorothy assured him that he wouldn't have to eat honeybees. The Sawhorse does consider himself superior and kick the Woozy, who claims to be a better steed and offers to burn the Sawhorse, an offer the Scarecrow refuses.
The Woozy doesn't make many notable appearances in the Famous Forty. He does join the grand expedition to find Ozma in The Lost Princess of Oz, most notably being able to walk over thistles thanks to his leathery skin.
Kim McFarland gave the Woozy an origin in A Refugee in Oz, but he doesn't seem to be very active in later Oz stories, instead just being one of the curious creatures you might find in Ozma's palace.