It would feel a bit strange to say Finland was Nazi during Winter War because during Continuation War Finland was Axis aligned when the USSR attack in Winter War is the biggest reason Finland sought closer ties with Germany.

Using something happened in 1918 and especially 1941 to justify calling Finland Nazi during Winter War that happened in 1939-40 seems fairly creative.

Interesting thing about the Civil War and Winter War though. After the Civil War Finland was heavily divided nation for a long time. And while the wounds had started to heal some, it was the opposition to the Soviet attack that actually brought the left and right together. I’m not sure how true it is, but I’ve heard Stalin expected the Finnish workers to celebrate him coming over and “freeing them” and was quite surprised that they were having none of that.

I honestly see it a lot more from people outside of Finland. And we often cringe at that too.

“Oh you’re from Finland? Kimi Räikkönen Simo Häyhä Winter War you win against USSR right??”

“…”

That’s not Winter War, that’s Continuation War. Simo Häyhä didn’t fight in Continuation War. As for war aims during Continuation War, the answer is obvious, to defeat USSR. It’s like asking why Germany bombed the UK.

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."