Who saidwars are won or lost on the playing fields of Eaton?

Nobody said that.

The Duke of Wellington is often quoted as saying "The battle of Waterloo was won on the playing fields of Eton". Eton is the school (equivalent to high school) where most of the British officer class of Wellington's day were educated, and the playing fields specifically would be where the values of good drill, courage and teamwork would have been inculcated into them.