'rosy-cheeked' is a compound formed from 'rosy' and 'cheeked'. 'rosy' originates from English 'rose' + the adjectival suffix '-y' (meaning 'having the quality of'), and 'rose' ultimately comes from Latin 'rosa' (via Old French 'rose'), meaning the flower 'rose' and the associated pink/red color. 'cheeked' is formed from the noun 'cheek' + the past-participial/adjectival suffix '-ed'.

'rosy' developed in Middle English from Old English/Norman-influenced forms of 'rose' and the suffix '-y' to mean 'rose-colored' or 'having the color of a rose'; 'cheek' comes from Old English (e.g. 'ceace' / 'ċēace') meaning the side of the face, and the adjective-forming '-ed' was added to create descriptive compounds like 'cheeked' (as in 'rosy-cheeked'). Over time speakers combined the two elements into the compound adjective 'rosy-cheeked'.

Originally 'rosy' primarily referred to the color of the rose (rose-colored); over time it extended to describe a pink or healthy complexion. Combined as 'rosy-cheeked,' the phrase came to mean specifically having pink or flushed cheeks, often implying health or vitality.