The swedes, norwegian, french, and brits were all on the finns' side AGAINST the russians. Even though the russians were allied with the USA against the nazis.
It's even more tangled than that. The Winter War started during the so-called "Phony War" of 1939. Remember this was BEFORE France fell, BEFORE the Battle of Britain, BEFORE US involvement, etc. Germany and the USSR were NOT fighting each other. They had divided the East between them.
That was the stage as it was set, and Stalin had secured a tacit agreement from Hitler to let him gobble up little Finland, along with the Baltic states. The mighty Red Army, by far the largest in the world, came down on Finland like the Golden Horde. The USSR had no other wars going on. There was no ostfront, no drain on resources. 100% of Soviet power was directed against a tiny arctic nation. Just as with Georgia today, the West wrung its hands. The Brits and Roosevelt issued stern statements. The USSR was booted from the League of Nations. But promises of supplies and hopes for support never materialized into actual rifles and artillery. It was Finland standing alone.
Then something amazing happened. Something absolutely nobody, from Hitler to Stalin to Roosevelt, ever expected. The Red Army did not sweep over the little country. The millions of men and thousands of tanks did not smash through the lines. The lines held at the pinch point in the south. To the north, the endless columns of Soviet power got bogged down on narrow dirt roads. The Finns struck back, moving fast and using their superior knowledge of conditions. They chopped the columns into "motti"--cord wood. Then they blocked the roads between the motti and pinned them down. Where the Soviets resisted, they kept them isolated and let them die. Terrible things happened to the soldiers trapped in those motti.
The weather went from cold to very cold to arctic cold--forty or more below zero. Physics change at those temperatures. The wool uniforms of the Soviets were designed for eastern European wet and mud, not for this kind of weather. Squads would simply freeze solid after falling asleep. And always the "white death" could come. Simho Hayha was far from the only Finnish marksman. Finland at that time was a nation of riflemen, most of them from small farms. The kind of people who always seem to make the best soldiers.
The war dragged on into 1940, but Stalin could not afford to give up. He brought in new troops, new commanders and better tanks and heavy weapons. Faced with a war it could not win in the long run, Finland agreed to give up Karelia and some other holdings. Russia still controls the land they took.
In the mean time, the world political situation changed completely. France fell, Hitler invaded the USSR and the US was brought into the war after Pearl. The next conflict saw Finland as a co-belligerent of Germany in an effort to reclaim Karelia. It was a side-show to the main event at that point, and drug on for several years. It is interesting to note that while Hitler tried to get Finland to Nazify, give up her Jews and so on, Finland simply said "thank you, no." They kept their parliament and did not become fascist. It's the only example I know of where a democratic nation worked with a fascist one during that war. In fairness we had abandoned them, and Germany was the only source of supplies they could reliably turn to. It's also interesting to remember that while Stalin was always paranoid about Finland attacking Leningrad from the north, they had no interest in doing so and never did during that whole war. They just wanted their land back.
Then the world shifted again, and Germany collapsed. Finland was placed firmly under Stalin's boot. While the USSR never annexed the nation, it was "Finlandized." The Finnish troops attacked the German units left in the country during the closing months of the war, and Karelia went back to Russia again.
The little wars had a big impact. Particularly the Winter War (Talvisota). Here are but a few:
--Hitler realized that the Russian bear was nowhere near as strong as he thought, and the Finnish victories made him contemplate a full-scale invasion of the USSR.
--Stalin realized the purges of the late 30's had badly weakened his military. The officer corps was revived, the political officers pulled out of front line power, and training emphasized more.
--The Red Army realized its tactics and materials were terribly inadequate. The failure of earlier tanks in Finland made them focus on the new T-34. Aircraft were replaced, and heavy weapons improved.
--The Red Army realized the importance snipers could play, and started training them in huge numbers. These became the bane of the Germans at Stalingrad and during the invasion of the Reich.
--Back in the US, the stories of the Civil Guard ski patrols led to the creation of the 10th Mountain Division and helped lay the foundation for America's elite units.
There's a recent documentary called "Fire and Ice" that's worth seeing:
http://www.youtube.com/watch?v=aCf8i2Gjgis&feature=related
Also, Will Trotter's "Frozen Hell" is the best general book on the subject. There's a recent book out called "The Winter War" that looks at it from the political context.