A horse that kicks and winces in impatience; figuratively, a wife (grey mare). Taylor, the water poet, calls it kicksie-winsie, but Shakespeare spells it kicky-wicky.
He wears his honour in a box unseen That hugs his kicky-wicky here at home, Spending his manly marrow in her arms, Which should sustain the bound and high curvet Of Mars's fiery steed.
All's Well that Ends Well, ii. 3 (Globe ed.).
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894