Etymology
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winter (n.)

Old English winter (plural wintru), "the fourth and coldest season of the year, winter," from Proto-Germanic *wintruz "winter" (source also of Old Frisian, Dutch winter, Old Saxon, Old High German wintar, German winter, Danish and Swedish vinter, Gothic wintrus, Old Norse vetr "winter"), probably literally "the wet season," from PIE *wend-, nasalized form of root *wed- (1) "water; wet"). On another old guess, cognate with Gaulish vindo-, Old Irish find "white." The usual PIE word is *gheim-.

As an adjective in Old English. The Anglo-Saxons counted years in "winters," as in Old English ænetre "one-year-old;" and wintercearig, which might mean either "winter-sad" or "sad with years." Old Norse Vetrardag, first day of winter, was the Saturday that fell between Oct. 10 and 16.

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grim (adj.)

Old English grimm "fierce, cruel, savage; severe, dire, painful," from Proto-Germanic *grimma- (source also of Old Saxon, Old Frisian, Old High German, German grimm "grim, angry, fierce," Old Norse grimmr "stern, horrible, dire," Swedish grym "fierce, furious"), from PIE *ghremno- "angry," which is perhaps imitative of the sound of rumbling thunder (compare Greek khremizein "to neigh," Old Church Slavonic vuzgrimeti "to thunder," Russian gremet' "thunder").

A weaker word now than it once was; sense of "dreary, gloomy" first recorded late 12c. It also had a verb form in Old English, grimman (class III strong verb; past tense gramm, past participle grummen), and a noun, grima "goblin, specter," perhaps also a proper name or attribute-name of a god, hence its appearance as an element in place names.

Grim reaper as a figurative phrase for "death" is attested by 1847 (the association of grim and death goes back at least to 17c.). A Middle English expression for "have recourse to harsh measures" was to wend the grim tooth (early 13c.).

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