If Stalin had waited little longer, he would have received information from his spies in Paris showing how ill-prepared the Allies actually were with all their plans regarding Finland. Other option was of course that Soviet spies had been more efficient. Finns had received the same information few weeks earlier and that had contributed to our willingness to sign the peace. Having that information might have persuaded Stalin to continue the war little longer and see what happens.
Finland will probably last few weeks more until its army totally collapses, though by then it has already retreated further west than the modern Russo-Finnish border. The situation in areas still controlled by the government will get chaotic as people will attempt to escape towards west away from the Red Army. Those who can will attempt to flee to Sweden. Sweden might attempt to occupy the Åland Islands, which Stalin might be even willing to accept as the man had strange sort of respect towards Swedes. I think the issue even came up in some unofficial discussions between Swedes and the Soviets but my memory being rusty take that with a pinch of salt.
It’s possible that in this sort of late Soviet victory scenario Finland might actually retain its nominal independence, at least for a while, though that depends much on Stalin’s whims. He can annex the country little later when the world’s attention is somewhere else after-all. At least few hundred thousand Finns will be moved to Siberia, in addition to those who had been executed during initial purges.
I don’t think there will be that significant effects on the Allies at this stage yet. Daladier will probably resign due to his inability to help Finland, as he did IOTL, and very soon the Norwegian Campaign will take the world’s attention. I suspect that we might be seeing first butterflies during that operation, but I must admit that I don’t have enough in-depth knowledge of that campaign to really comment anything.
Regarding Barbarossa, the Soviets have now a shorter front and have freed about 10-20 divisions to be used elsewhere. Some of those would be needed in Finland though to, to prevent German amphibious landings and against their forces in Norway, in addition to general pacification operations in the country. Probably few troops on the Swedish border too, just in case.
Sweden’s position ITTL is highly interesting, I think. They would be certainly experiencing much more pressure from all sides of the war due to their new geopolitical status. Germans would be probably still interested in moving their troops trough the country but now Sweden has also the Soviet Union as their neighbor to consider.
One interesting source of butterflies is also nickel mines in Petsamo, in Northernmost Lapland. Petsamo was one of the most important sources of nickel in the world during the WW2. While the production was just starting in the late 1930’s, it rapidly increased during the war and by 1943 it provided 73% of Germany’s nickel consumption. By 1944 this had increased to 87%. This might cause some butterflies regarding the German war production during the war. Just like the Soviets IOTL were able to defend their front in Kola very effectively, Petsamo would be just as defendable.