This myth always gets perpetuated when Lenin himself allowed Finland to freely dissociate themselves from the USSR upon its founding (a grave mistake!). The Winter War was fought more or less over the question of "will you at least commit to not letting Nazis pass through your country to invade the USSR yes or no," which the Finns chose to answer by siding with the Nazis and giving Nazis passage over their land, giving an advantage to the Nazis (this is bad, if you aren't following at home) that could have been avoided.
I did not expect this to leave my immediate friend group, but since someone linked this on Setz's response, I will link the sources from which I draw my claims (previously thought to be unneeded since my immediate social group is already familiar). In fact, I don't even have to use sources that are overly deferential to the USSR, as we'll see.
This was the soviet demand, from a Finnish source in 1940:
“In the negotiations with Finland, the Soviet Union is mainly concerned with the settlement of two questions:
a) securing the safety of Leningrad;
b) becoming satisfied that Finland will maintain firm, friendly relations with the Soviet Union.
In order to fulfil this duty, it is necessary:
(1) To make it possible to block the opening of the Gulf of Finland by means of artillery fire from both coasts of the Gulf of Finland in order to prevent warships and transport ships of the enemy penetrating, to the waters of the Gulf of Finland.
(2) To make it possible to prevent the access of the enemy to those islands in the Gulf of Finland which are situated west and north-west of the entrance to Leningrad.
(3) To have the Finnish frontier in the Karelian Isthmus, which is now at a distance of 32 km. from Leningrad, i.e., within the range of long-distance artillery, moved somewhat farther northwards and northwestwards”.
(‘The Development of Finnish-Soviet Relations of 1939″;Helsinki 1940; p. 49-50).
This is, of course, with Nazis rapidly advancing into Soviet land.
The Finnish internal position was this:
“If the Soviet Union should make proposals regarding the creation of Soviet Union military bases on the Finnish mainland, or, e.g., on the Aaland Islands, such proposals should be rejected and any discussion thereof refused. The same applies to any proposals referring to frontier adjustments on the Karelian Isthmus. . . . .
If the Soviet Union suggests the conclusion of a treaty of mutual assistance, . . it should be pointed out that such a treaty is not compatible with Finland’s policy of neutrality”.
(‘The Development of Finnish-Soviet Relations . . . ‘; ibid.; p.47, 49).
To this end, Stalin offered Finland an exchange of land:
“It is not the fault of either of us that geographical circumstances are as they are. We must be able to bar entrance to the Gulf of Finland. . . . .
Once a hostile fleet is in the Gulf, the Gulf can no longer be defended.
You ask what power might attack us. England or Germany. We are on good terms with Germany now, but everything in this world may change. Yudenich* attacked through the Gulf of Finland, and later the British did the same. This can happen again. If you’re afraid to give us bases on the mainland, we can dig a canal round Hanko Neck. .
We ask that the distance of Leningrad to the line should be 70 kilometres. That is minimum demand, and you must not think we are prepared to reduce it bit by bit. We can’t move Leningrad, so the line has to move. . . . We ask for 2,700 square kilometres and offer more than 5,500 in exchange”.
(V. Tanner: ‘The Winter War: Finland against Russia: 1939-1940’; Stanford (USA); 1957; p. 27-28).
This was rejected by the Finnish authorities. The Winter War was never a defensive one on Finnish part. There was no grand conspiracy to subsume all of Finland. In fact, this is echoed even in history relatively hostile to the USSR in the 1950s:
“The Soviet leaders were determined, above all, to do two things.
They wished to push the frontier on the Karelian Isthmus back a substantial distance from its closest approach to Leningrad. . . .
They also wished to establish a naval base on the Finnish coast at the mouth of the Gulf, opposite the newly acquired bases in Estonia, so that any hostile shipping coming up the Gulf of Finland would have to run the gauntlet of a cross fire”.
(C. L. Lundin: ‘Finland in the Second World ‘; Bloomington (USA); p. 51-52).
The truth of the matter is, Finland, whose anticommunist stance (and its strategic position in an invasion of USSR) was well known to all of the world* saw that Nazis were rapidly advancing into Russia and decided that they should throw their lots in with the Nazis. If even historians mostly hostile to the USSR could agree on this in 1957, then people in the 2020s could stand to do a lot better in studying history.
*Times Magazine noted as early as April of 1919 that Finalnd would be the best way to attack Leningrad, into Moscow from Leningrad.