I started thinking about the actual timeline of the events if Finland caved in and then was gradually Sovietized. Going by the Estonian example, it might go something like this:
Early November 1939: Finnish government accepts moving border west on the Karelian isthmus, handing over parts of Kalastajansaarento in the north and several islands on the Gulf of Finland, as well as leasing the Hanko Peninsula to the USSR for 30 years for military use. Flags are flown at half mast across the country. Protests in major towns by those opposed to the decision, left wing counter protests organised by the Finnish Communist Party lead to clashes with the police.
Mid-November 1939: Finnish troops are withdrawn from the areas to be ceded to the USSR and local civilians flee west to escape Soviet rule. A Soviet flotilla arrives at Hanko to take over the "lease area" and start preparations to build a military base. Moscow protests the recalcitrance of Finnish soldiers and officials, demands the Finnish armed forces stand down and that uncooperative elements are removed.
Prime Minister Cajander resigns under pressure and parts of the army are demobilized. The Soviet embassy delivers President Kallio a list of acceptable ministers for the new cabinet. Kallio appoints Risto Ryti (Progress Party) as Prime Minister of a wide-based coalition cabinet.
December 1939: The ceded areas have been emptied and are taken over by Soviet units. Upon seeing reports that farmhouses have been burned down and factories and military installations have been sabotaged, Moscow heavily chastises the Finnish government for not adhering to the letter of the recent agreement and the "spirit of Finno-Soviet cooperation". Large left wing demonstrations continue in major towns, leading to more violence between the protestors and the police, now supported by righ-wing members of the Civil Guard.
The new Ryti cabinet is under a constant barrage of demands and protests from the Soviet leadership. President Kallio has long been suffering from ill health, and just before Chrismas he suffers a stroke that leaves him incapacitated. Ryti takes over as acting President.
January 1940: The construction of the Soviet naval base in Hanko continues, though slowed down by the sea freezing. Coastal and sea area reserved for Soviet use extended after a Finnish armed icebreaker accidentally opens fire on a Soviet ship, causing yet another diplomatic row. Late in the month, Soviet Foreign Minister Molotov demands that the recently founded Society for Finno-Soviet Friendship and Peace be allowed under the Finnish law, together with other Socialist and Communist organisations, and that the extreme right and "militarist organisations" be curbed.
February 1940: Soviet aircraft are breaching the Finnish airspace on a daily basis, while Moscow claims that the Finns show habitual disrespect for the new borders. Moscow is delivering the Finnish leadership lists of military officers that need to be removed from their posts in the interest of peace, including Mannerheim. Taking away the Petsamo nickel mine concession from the Canadian INCO-Mond and setting up a joint Finno-Soviet mining company instead demanded by Molotov. President Kallio suffers another stroke and resigns the presidency citing health reasons. Ryti voted President by the parliament in a special election.
March 1940: Ryti's offer of a neutrality-based, defensive alliance between Finland and Sweden shot down by Stockholm, Moscow and Berlin. The Swedish demand for an alliance would have included Finland forsaking the possiblity of the return of the territories so far relinquished to the Soviets "in perpetuity"; unacceptable by the Finns. Finnish officers and members of the Civil Guard begin preparations for guerrilla war against a possible Soviet occupation; weapon caches are built in forests and the countryside. General Airo is the primus motor of the secret plans.
April 1940: The Spring Crisis - the Soviet Embassy finds out about high-level contacts between the Finnish military and representatives of Göring; Molotov travels to Berlin to demand that Germany holds its part of the Molotov-Ribbentrop deal. Hitler assures Molotov that the USSR has "free hands" in Finland. Moscow keeps the Finnish government in a diplomatic vise also in other ways, for example claims acts of sabotage against trains carrying Soviet military personnel between Hanko and the border. Socialist and Communist organisations officially reallowed in Finland.
Most of the Finnish Army demobilized and several leading officers sacked. The spring sees a sharp increase of Finns leaving the homeland for Sweden as emigrants. Officers and military specialists start disappearing from garrisons for "personal leave of absense", finding their way alternately to secret forest "bases" or Sweden.
May 1940: Soviet aircraft start flying between a newly-built Hanko airstrip, the Estonian coast and Leningrad within nominally Finnish airspace. Finnish Air Force demanded to respect new "no-fly zones" after it tries to intercept these aircraft. Later in the month, entire FAF units grounded due to political pressure. Concentrations of Soviet troops reported on the Isthmus before the planes are grounded.
June 1940: A joint naval blockade of Finland and Estonia by the Red Navy started, Finnish navy ships ordered to stay in port. Two weeks into the month, Molotov delivers an ultimatum to the Ryti government, accusing it of conspiring with the Baltic states and Germany against the Soviet Union. Soviet units breach Finnish borders in southern and northern Karelia while Soviet bombers are daily seen flying low above Helsinki.
The Finnish cabinet mulls a declaration of war while large Communist demonstrations again rock the capital. Upon hearing that a Soviet military convoy has left Hanko unopposed and will arrive to the capital in hours, the cabinet decides not to declare war to avoid unnecessary bloodshed in the face of overwhelming force. Orders are given for the already diminished army to stand down - not always successfully. In North Karelia, a small border force holds back an entire Soviet division for hours before being forced to surrender.
The Ryti cabinet forced to resign at gunpoint in the quickly occupied capital. Sporadic resistance by members of police and Civil Guard quikcly overwhelmed. Parliament flees Helsinki, or those MPs that can. Emigrant Communist Otto Ville Kuusinen arrives at the capital on a special flight to start preparations for new elections for a parliament "more in tune with the will of the people".
Before the end of the month, southern Finland is occupied by Soviet troops and quick "elections" held in which only Communist candidates are allowed. Most of the "elected" are emigrants who just recently arrived back from the Soviet Union.
In the countryside and in the north, the Soviet control is more sporadic, and in several cases the "secret army" and irregular Civil Guard units have started engaging the occupier, scoring tactical victories in places.
July-August 1940: Kuusinen declares the "Finnish Democratic Republic" in Helsinki, signs a treaty of friendship and cooperation with Molotov. The Red Army continues operations to pacify the Finnish towns and the countryside. In the countryside the resistance just seems to stiffen, causing more and heavily armed units to be sent to help. Entire villages destroyed to root out the resistance. Newly-founded Finnish People's Police and the NKVD start a wave of arrests in major towns, cargo trains standing by to take those arrested east. Politicians, military officers, leading businessmen especially targeted.
Refugees are now leaving Western Finland in droves, going to Sweden by all available ships and and boats, by car, horse cart and on foot in the north. Some Finnish warships manage to leave port unannounced and head for the Swedish coast, sometimes getting caught by patrolling Red Navy vessels. By the end of the month, most major ports in Finland are in Soviet control and by the end of the summer the Soviet troops control the border crossings towards Sweden.
In Stockholm, Svinhufvud, Tanner and Mannerheim (or other similar figures) announce a Government of National Unity in Exile, promising for the Finnish people to keep up the fight against the occupier. More politicians and leading soldiers join the group if they manage to elude capture or have already left Finland in time.
The Swedish government protests the events in Finland. Swedish ships arrive at the Åland islands, but turn back after being greeted by warning shots across the bow by the Soviet warships outside Mariehamn, there to protect the "Finnish Democratic Republic's" claim to the islands. Sweden refrains from declaring war but dismisses the Soviet ambassador.
It will be a very cold autumn around the northern Baltic Sea.
Would this sound plausible?