Technically, no, there is not a game-ending event.
There is a cutscene that plays on the first day of Year 3, a sort of "evaluation", but that doesn't end the game.
And there is a cutscene that was added in 1.5 after completing most elements of the game, but that doesn't stop gameplay either.
Really, you can be finished whenever you want, which is great!
There is always the option to start another farm, on a different farm layout, with a different farmer, and so you could keep playing forever. Alternatively, you could play on the same farm indefinitely, which is cool too! ;D