Green’s Dictionary of Slang

winey adj.

tipsy, slightly drunk.

[UK]T. Hood ‘China-Mender’ Works (1862) II 435: It was all through Mr. Lambert : but for certain he was winey.
[UK]Dickens ‘Slang’ in Household Words 24 Sept. 75/2: For the one word drunk [...] muggy, beery, winey, slewed [etc.].
[UK]Hotten Dict. of Modern Sl. etc.
[UK]London Standard 13 Dec. 3/3: Slang synonyms for mild intoxication [...] Stewed [...] Winey.
[UK]Sl. Dict.
[US]Salt Lake City (UT) 30 Mar. 4/5: He is [...] happy, winey, groggy, muzzy .
[UK]Farmer & Henley Sl. and Its Analogues.
[Aus]Crowe Aus. Sl. Dict. 96: Winey, tipsy; intoxicated.
[UK](con. c.1916) A. Harding in Samuel East End Und. 119: He was a bit winey.