I would have guessed the win- element was related to win. It is but not to the common win, rather to an obsolete win meaning joy, pleasure, delight. OED has the details:
Etymology: Old English wynsum = Old Saxon wunsam , Old High German wunnisam (Middle High German wun(ne)sam ), < wyn(n win n.2 + -sum -some suffix1. Sense 3 came into the literary language from northern dialects
.Etymology: Old English wyn(n , corresponding to Old Saxon wunnia , Old High German wunnja , wunna strong feminine, wunnî < and wunno weak masculine (Middle High German wünne , wunne , German wonne ); < Germanic wun- , found also in Old English gewun , wunian (see wont n.1), wýscan ( < *wunskjan ) to wish v., and related to wen- (see ween n., ween v.) and wine n.2, friend.
As for the common win that comes from Old English winnan, to win, to obtain. BTW lovely word mentioned in that etymology, witherwin, which OED defines as “an enemy, adversary; spec. the Adversary, the Devil”.
Ah well, you win some, you lose some.