hoof (n.) Look up hoof at Dictionary.com
Old English hof "hoof," from Proto-Germanic *hofaz (cognates: Old Saxon, Old Frisian hof, Old Norse hofr, Danish hov, Dutch hoef, German Huf "hof"), from PIE *kop- "to beat, strike" (cognates: Sanskrit saphah "hoof," Polish kopyto "hoof;" see hatchet (n.)). For spelling, see hood (n.1).
A hoof differs from a nail or claw only in being blunt and large enough to inclose the end of the limb; and almost every gradation is to be found between such structures as the human nails, or the claws of a cat, and the hoofs of a horse or an ox. The substance is the same in any case, and the same as horn, being modified and greatly thickened cuticle or epidermis. [Century Dictionary]
Hoof-and-mouth disease is attested from 1887. Phrase on the hoof is from 1750 as "walking;" later it was cattlemen and butchers' slang for "not (yet) slaughtered."
hoof (v.) Look up hoof at Dictionary.com
"having hoofs (of a specified kind)," c. 1500 in compounds, from hoof (n.). Meaning "to walk" (as in hoof it) is from 1640s; slang meaning "to dance" is 1920, American English (implied in hoofer). Related: Hoofing.