Whoa! Neat is another name for cattle.
Neatsfoot oil is a yellow oil rendered and purified from the shin bones and feet (but not the hooves) of cattle. "Neat" in the oil's name comes from an old name for cattle. Neatsfoot oil is used as a conditioning, softening and preservative agent for leather. In the 18th century, it was also used medicinally as a topical application for dry scaly skin conditions.
"Prime neatsfoot oil" or "neatsfoot oil compound" are terms used for a blend of pure neatsfoot oil and non-animal oils, generally mineral or other petroleum-based oils.
I am familiar with bull, ox, steer, calf, cow and even kine (the ancient plural for cow). But I have never heard the word "neat" used that way.