Was WWII....

[Foreigner]

Then, What if France and Britain would have send the expeditionary force to Scandinavia at the time of Winter War, securing Norway, Sweden, and entering Winter War against USSR?

The French mountain troops were already embarking their ships when Winter War ended...

Well, Britain did send out an expeditionary force to Scandinavia at some point, didn't they? Let's take that as a basis for analysis. Imagine the Norway campaign, but with several hundred miles further to move troops and supplies - through difficult terrain and harsh climate, and to be able to reach the theater by sea, either to have to sail all around Scandinavia through the Arctic Ocean (in winter, no less) or to force through the Baltic Sea by both Germany and the Soviets; to have to violate the neutrality of two countries (and potentially to have to endure some form of resistance both from communist and nationalist groups); and then to face not an expeditionary force, but a potentially significant part of one of the largest land armies in Europe (that did not rely much on sea communications that could be cut) - even though on a unit basis not up to the quality of the German units in the Norway campaign. With all due respect to the Finns fighting for their homeland, with any support that Britain and France could muster at the time, they might have inflicted disproportionately larger losses on the Soviets, but I doubt they would have changed the outcome much. I think the actions of the Soviets during the Winter War showed that they were willing to pay the potentially higher cost for the victory.

Looking at it from another angle, while the Finns ended surrendering territories, they were not utterly defeated at the end of the war, so they had potential for further resistance. So if Britain and France were that serious about helping them, they could have reinforced the Finns and tried to push the Soviets back - but they didn't. The most logical explanation (for me) is that they understood that any help of theirs would not make much of a difference.

On a side note about the French mountain troops - well, I guess the logic might have been that they would be more used to the cold, as there were (to the best of my knowledge) no mountains in the area of the fighting. However, mountain troops do imply lack of serious heavy weapons, which would handicap them when dealing with Soviet tanks.

The more serious potential for material impact of a move to attack the Soviets in the Winter War would be to signal to Germany "look, we are both against Bolshevism, let's band together". But while this is possible, I would still find it highly unlikely. Especially for Britain I think it would be too sharp an about-face for the public to accept - to side with a regime that so far had been vilified, and whose U-boats had been waging unrestricted warfare against British shipping (that immediately brought back memories of WWI). On the other side, Hitler distrusted Britain and France (that's why eventually he moved to defeat them first). So while there were certainly circles on both sides that favored an alliance against the Soviets, I think the majority view in Britain would be better exemplified by the famous Churchill quote about Hitler and the devil.

In such an environment, then, an attack on the Soviets (in addition to participation in the Winter War, bombing of the Baku oil fields had been considered) would likely be interpreted as an attack on a German ally (no matter how insincere the relationship) - and, in the case of a Scandinavian landing - an attempt to cut the supply of Swedish iron ore. So we might see a combined Norway and Sweden campaign happening earlier than in actual history.

On the Soviet side, as a result of the attacks the media might "suddenly remember" that Britain and France had participated in the intervention on the "White" side in the Civil war after WWI (while Germany did not) - and equally "suddenly forget" the more recent "proxy" Spanish Civil War. So maybe rapprochement between the Reich and the Soviets could have gotten stronger, although not by much.

Now I consider what I am about to describe below as an unlikely scenario, but it seems this thread has left the bounds of reason far behind already.

Assuming Stalin was willing to offer and Hitler willing to accept direct military assistance, we mighty have seen a joint push into Scandinavia (and subsequent partitioning according to the Polish scenario). At the extreme, we might have seen a Soviet expeditionary force join the attack on France in the summer of 1940. Pushing the extreme further, we might have even seen what was in actuality "Vichy France" become (at least partly) a Soviet "occupation zone". But, alternatively, the presence of significant allied forces might have reduced the incentive for the German command to accept the unorthodox pan of attacking through the Ardennes, which could mean none of the Blitzkrieg, but a more conventional WWI-style slugfest.

Pushing the extreme to ridiculous levels, it is possible that in the meantime both Germany and the Soviets would realize that by cooperating they could gain most benefits of a conquest without the risk and expense of actual fighting - and the Eastern Front never happens. However, I don't think the two leaders would be ever able to trust each other sufficiently - so they would likely have had to come to blows sooner or later.