O.E.
ate "grain of the oat plant" (pl.
atan), possibly from O.N.
eitill "nodule," denoting a single grain, of unknown origin. The usual Gmc. name is derived from P.Gmc.
*khabran (cf. O.N.
hafri, Du.
haver, source of
haversack). Famously defined by Johnson as, "A grain, which in England is generally given to horses, but in Scotland supports the people."
Wild oats, "crop that one will regret sowing," is first attested 1564, in ref. to the folly of sowing these instead of good grain.
"That wilfull and vnruly age, which lacketh rypenes and discretion, and (as wee saye) hath not sowed all theyr wyeld Oates." [Thomas Newton, "Lemnie's Touchstone of complexions," 1576]
Hence, to
feel (one's) oats "be lively," 1831, originally Amer.Eng.
[oht] 
) the seed of this plant, used as a food for humans and animals.