冬編笠に夏頭巾
(Fuyu amigasa ni natsu zukin; “Woven hats in winter; hoods in summer”)

Definition:

Things are the opposite of how they should be. Left is right, dogs are cats, up is down, people wear hats that don’t match the season, and elected officials who used to claim they cared about the law are openly supporting and defending a criminal.

Breakdown:

We begin three characters in with the noun 笠 (kasa), your classic conical hat, compounded with and modified by verb-stem-acting-as-noun 編 (here ami), “knit,” “braid.” The woven hat is further modified by noun 冬 (fuyu), “winter.”

Similarly, the latter noun phrase centers around 巾 (kin), a rectangle of cloth, modified by noun 頭 (here zu), “head,” and this compound in turn modified by the noun 夏 (natsu), “summer.”

The two compound nouns are joined by particle に (ni), apparently functioning as a directional particle and thus literally “to,” but better read in the sense of “added to,” i.e. “and.”

Notes:

Wide-brimmed woven hats allow a breeze through and keep off the hot sunlight; a zukin essentially serves the same function as a stocking cap, although as a piece of cloth wrapped around the head it can take a variety of shapes.

An alternate version of this phrase replaces headwear with bodywear: the inappropriate winter wear becomes 帷子 (katabira), a light single-layer kimono, and the summer wear becomes 布子 (nunuko), clothing insulated with cotton padding. Also compare and contrast with 夏炉冬扇.

One style of amigasa, from a mid-1970s TV drama, eponymously titled Amigasa Juubei (編笠十兵衛)

One style of zukin, from the same show

A selection of zukin styles from Kotobank, including possibly the dorkiest hood ever

Example sentence:

「あの無責任な奴が強い権力を持っているなんて、冬編笠に夏頭巾だ。我々の組織はこれでもはや絶望的な状態だ」

(“Ano musekinin na yatsu ga tsuyoi kenryoku wo motteiru nante, fuyu amigasa ni natsu zoukin da. Wareware no soshiki wa kore de mohaya zetsubouteki na joutai da.”)

[“For that irresponsible a-hole to have so much power, everything is upside-down and backwards. With this, our whole organization is in desperate straits.”]