To quote from Red Star (Krasnaya Zvezda/Кра́сная звезда́, the Soviet army newspaper), 2nd December 1939:

We will help the workers of Finland to free themselves from the oppressors!

Death to provocateurs of war!

According to Soviet internal (and external) propaganda, Finland started the war, by shelling a Soviet border post at Mainila. The Finnish government - hard-core Whites one and all - pushed the peace-loving Soviet leadership into war, first by threatening the security of Leningrad and wanting to grab all of Karelia (i.e., the parts in the Soviet Union) for Finland, second by unreasonable stubbornness in the negotiations before the Winter War, and third by killing soldiers of the Red Army at Mainila. Clearly, this kind of thing had to be punished!

And since the Finnish government was hard-core Whites, the victors of the Finnish Civil War, who were oppressors and bloody torturers of the Finnish working classes, there was a humanitarian aspect to it: the liberation of the Finnish working class, long overdue since their bloody defeat in the Civil War.

While the above is from internal propaganda, this propaganda was effective, and many Soviet soldiers believed it to be a war of liberation when they went to Finland. This led to a certain amount of bewilderment - the bulk of the Finnish army was the working class, so how could they resist their own liberation so energetically?

Later in the war, Soviet soldiers had more realistic attitudes - they were fighting because it was important for their country to win its wars, regardless of why or how the wars had begun. In addition, after its poor performance early in the war, it was important to restore the honour and reputation of the Red Army. Uncritical patriotic support of their country, and patriotic support of their army replaced helping the workers of Finland overthrow their White oppressors as motivation for fighting.

There is useful discussion of Soviet internal propaganda in:

• James Venceslav Anzulovic, Jr., The Russian Record of the Winter War, 1939-1940: An Analytical Study of Soviet Records of the War with Finland from 30 November 1939 to 12 March 1940, PhD thesis, University of Maryland, 1968

• Carl Van Dyke, The Soviet Invasion of Finland, 1939-40, Routledge, 1997

The quote from Red Star is from https://histdoc.net/history/press.html which has a range of relevant documents from the contemporary press, in both the original languages and English translation. These include 4 war poems https://histdoc.net/history/1940_stihi.html within which the following lines can be found:

Suomi, your salvation lives only within us,

only we bring liberation to the working people

The recent discussion of the pre-war negotiations might be of interest if you missed it the first time around: https://www.reddit.com/r/AskHistorians/comments/b4s3mo/finland_famously_did_disproportionately_well/