Finland in the winter war was a fascist state allied with Germany

No, you are thinking of Continuation War. During Winter War Finland wasn’t allied with Germany, rather contrary to that Germany was hampering some efforts to ship armaments to Finland because of Molotov-Ribbentrop. Not only that, Finland wasn’t at all fascist. It was a functioning multi-party democracy.

Finland was effectively a German puppet state by the time the Soviets invaded in 1939.

That has no basis in reality. I suggest you read this article that gives some basics about the background for Winter War https://en.wikipedia.org/wiki/Background_of_the_Winter_War

See for example: "Finnish–German relations cooled after the National Socialist Party rose to power in Germany in 1933. Finns admired Imperial Germany, but not the radical and antidemocratic Nazi regime. Finnish conservatives did not accept the Nazis’ state violence and antireligious policies. Still, there was sympathy for German aims to revise the Treaty of Versailles, but the official Finnish policy was reserved, especially after the German invasion of Czechoslovakia. Finland even recalled its ambassador for a short period.

Finnish Nazis and ultranationalist parties such as the Patriotic People’s Movement achieved only minor support in several elections, especially in the aftermath of the failed Mäntsälä rebellion in 1932."