Hier ein interessante Hypothese, wie sich der Satz im Englischen ausgebreitet hat.
Nevertheless, the phrase isn't Tudor. A quick search of the World Wide Web will yield confidently expressed views that 'revenge is a dish best served cold' is a translation of the line "La vengeance est un plat qui se mange froide" from Pierre Choderlos de Laclos's epistolary novel Les Liaisons Dangereuses, 1782. As that text doesn't appear in the novel, or any other work by de Laclos, the story appears to be a piece of impressively industrious folk etymology - not only a made up source, but made up in French [...and I understand from French corresponents that the 'froide' should be 'froid' - not a mistake that de Laclosmight have made].
Wherever it can be said to have originated, the proverb struck a chord in the English-speaking world. More recently, it has been called into use in three screen classics:
Kind Hearts and Coronets, 1949: "Revenge is a dish which people of taste prefer to eat cold."
The Godfather, 1969: Don Corleone nodded. "Revenge is a dish that tastes best when it is cold," he said.
Star Trek II, The Wrath of Kahn, 1982: Kirk, old friend, do you know the Klingon proverb, "Revenge is a dish best served cold"?