Fools and jesters used to wear a calf-skin coat buttoned down the back. In allusion to this custom, Faulconbridge says insolently to the Archduke of Austria, who had acted most basely to Richard Coeur-de-Lion-
Thou wear a lion's hide! Doff it, for shame, And hang a calf-skin on those recreant limbs.
Shakespeare: King John, iii. 1.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894