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.
The USSR wanted Finland to give it areas including the main Finnish defensive line. Knowing what happened with Czechoslovakia and “just a few areas” and knowing what happened to Baltics, it’s easy to see what road that would’ve taken Finland down on.
You’re saying the Continuation War happened solely because of the Winter War
No, I’m saying Finland sought help from the Nazis because during Winter War Finland was left completely alone, the preferred alliance direction of Nordics or UK/France/US panning out to not have done much at all. And both sides, USSR and Finland knew it was just a temporarily truce and another war was coming. Obviously Finland didn’t want to be alone, again.
the noted anti-communists were in no-way ideologically aligned with the Nazis before the USSR’s attack
Mostly the Finnish leadership were noted anglophiles.
wanted Finland to give it areas
And offered more area in Karelia in return, it wasn’t some kind of a one-sided deal