Hat

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Old English hætt, of Germanic origin; related to Old Norse hǫttr ‘hood’, also to hood1.

wiktionary

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From Middle English hat, from Old English hæt(“head-covering, hat”), from Proto-Germanic *hattuz(“hat”), from Proto-Indo-European *kadʰ-(“to guard, cover, care for, protect”). Cognate with North Frisian hat(“hat”), Danish hat(“hat”), Swedish hatt(“hat”), Icelandic hattur(“hat”), Latin cassis(“helmet”), Lithuanian kudas(“bird's crest or tuft”), Avestan 𐬑𐬀𐬊𐬛𐬀‎ (xaoda, “hat”), Persian خود‎ (xud, “helmet”), Welsh cadw(“to provide for, ensure”). Compare also hood.

hat

etymonline

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hat (n.)

Old English hæt "hat, head covering" (variously glossing Latin pileus, galerus, mitra, tiara), from Proto-Germanic *hattuz "hood, cowl" (source also of Frisian hat, Old Norse hattr, höttr "a hood or cowl"), of uncertain etymology; it has been compared with Lithuanian kuodas "tuft or crest of a bird" and Latin cassis "helmet" (but this is said to be from Etruscan).

To throw (one's) hat in the ring was originally (1847) to take up a challenge in prize-fighting. Toeat one's hat (1770), expressing what one will do if something he considers a sure thing turns out not to be, is said to have been originally eat Old Rowley's [Charles II's] hat.