Old English ate (plural atan) "grain of the oat plant, wild oats," of uncertain origin, possibly from Old Norse eitill "nodule," denoting a single grain, of unknown origin. The English word has cognates in Frisian and some Dutch dialects. Famously defined by Johnson as, "A grain, which in England is generally given to horses, but in Scotland supports the people."
The usual Germanic name is derived from Proto-Germanic *khabran (cf. Old Norse hafri, Dutch haver, source of haversack). Wild oats, "crop that one will regret sowing," is first attested 1560s, in reference to the folly of sowing these instead of good grain.
Hence, to feel (one's) oats "be lively," 1831, originally American English.