Besides, Soviets merely wanted the area around Leningrad, not to take the whole country.
Soviets wanted to better protect Leningrad as it was a major industrial center and a "City of the Revolution", bearing the name of Lenin, fearing an Axis attack from Finland.
"Stalin only wanted to take a bit of land to defend Leningrad" is Stalinist state propaganda and is to anyone who has studied the facts, as obviously false as the official reason by Hitler for invading Poland. Stalin had always wanted to retake the lands of the Russian Empire, and then some, which is the main reason
all of Finland was assigned to Russia in the Molotov-Ribbentrop Pact in the first place.
Here is a map from an excellent book called
The Soviet Plans for the Northwestern Theatre of Operations in 1939-44 written by Ohto Manninen, with this English translation of the original Finnish work being published by the
National Defence University of Finland, detailing the objectives of the Russian armies in November 1939 at the start of the Winter War:
It's also worth mentioning here that on the 29th of November 1939, the Leningrad Military District issued the following order: "When arriving at the borders of Sweden and Norway, these are not to be violated nor are provocations to be tolerated. The soldiers of the Swedish and Norwegian armed forces are to be saluted at the border.".
The Russian goal was the liquidation of Finland as an independent state, incorporating it into the USSR as a part of the
Karelo-Finnish SSR, originally the Karelian ASSR, but elevated to the status of SSR, with "Finnish" being added to its name, specifically for this purpose.
Of course since the Red Army failed, Finland continued existing as an independent and democratic state, as it has existed since 1917 (save for a brief period in 1918-19 when full democracy was de facto suspended due to the civil war and subsequent regency).
Speaking of failing, here is the actual progress of the Red Army in the Winter War:
Quite a ways to go to the Swedish border.
Of course Stalin, being a ruthless man with imperialist ambitions, did not give up with the military disaster and threat of Franco-British intervention that forced him to end the Winter War prematurely. Throughout all of the Interim Peace of 1940-41 Russia broke one peace clause after another: Finns were fired upon and kidnapped, a Finnish passenger plane was shot down and its contents looted by a Russian submarine, more land, including entire towns (e.g. the town of Enso), was taken than was agreed to in the peace deal signed in March 1940. Over time the Finns were given more and more demands, ranging from building railroads in conspicuously strategic locations, to handing over a share of the Kolosjoki nickel mine in Petsamo, and so on.
In the fall of 1940 with a build-up of Russian forces on the Finnish border and a serious threat of another Russian invasion, Finland accepted German offers of troop transit rights through Finland to its Norwegian possessions. This brought Finland under Germany's protection. Indeed when Molotov travelled to Berlin in November 1940, the right to "finish the job" with Finland, a dangerous nation of dangerous people, according to Molotov, was the first item on his list of demands to Hitler. Hitler rebuffed Molotov, saying Germany cannot tolerate another war around the Baltic Sea.
Actually when the Red Army shelled Finnish troops and bombed Finnish cities, towns and ships in June 1941, beginning the Continuation War, they were simply acting on the pre-existing war plan against Finland, pictured above. Of course the Russian ground forces could not fulfill even an attempt at a serious offensive because most forces were being transferred away from the Finnish frontier to face the German invasion.
I have already briefly described the decisive battles of summer 1944 and their aftermath in a previous post, but for the sake of completeness, I'll post one more picture, detailing the movements, and ultimately the destruction at the VKT and U-lines (both of which were incomplete, with the VKT-line fortifications being completely non-existent outside of the Viipuri area), of the Red Army's Karelian Offensive, whose objective was to push deep into Finland and force the unconditional surrender, and thus occupation and Sovietization of the country.
Apologies for the Finnish in the pictures, I used books I had readily available. Such exact detail on the Finnish front isn't very available in English anyway, particularly online. The images should speak for themselves though.