As you say, we’re limited to speculation when it comes to considering historical what-ifs, so it’s impossible to nail down what would have happened if Britain and France had joined Finland’s side in the Winter War against the USSR. For whatever it’s worth, however, here are some thoughts on the subject.
An important point to remember is that “going to war” during the WWII era took many different forms. The form we tend to think of is a full-scale general war, in which Power X invades the territory of Power Y on a massive scale with the aim of destroying its armed forces and conquering its territory; the German campaign against France in May-June 1940 was one such case, and the German invasion of the USSR in June 1941 was another one. There are other gradations of war, however. For example, Japan and the USSR fought a couple of undeclared, low-level wars with each other in the late 1930s along the borders of Manchuria and Mongolia. Those conflicts are little-known because they were short and localized and relatively inconsequential in terms of territory change…though they did have strategic importance, in the sense that they were part of the reason why Japan and the USSR eventually signed a non-aggression pact.
An even better example would be the Phony War phase of WWII, from September 1939 to May 1940, because it potentially parallels what might have happened if Britain and France had declared war on the Soviet Union to support Finland. “What might have happened” might actually have been “very little.” Britain and France declared war on Germany in early September 1939 to support Poland…but other than clearing German shipping from the sea, they basically sat on their hindquarters until the following spring, even though the border between Germany and France was minimally defended by Germany (whose army was concentrated in Poland). France did launch the so-called “Saar Offensive”, which basically involved a few French troops advancing a few miles into German territory. Their advance was unopposed. France and Britain got some great newsreel footage out of this, but they did little else; sometime later the French quietly withdrew back to the Maginot Line. Given how pathetically unenterprising they were at crossing the border between their own country and Germany (something which can be done with a single footstep), I find it hard to imagine that the French would have posed any credible threat to the Soviet Union if they had declared war against Stalin and had announced that they were going to send an expeditionary force to the Russo-Finnish border. Ditto for the British: during the Phony War, Chamberlain thought that the nasty business of combat could be avoided by, among other things, using RAF bombers to drop propaganda leaflets on Germany to convince its citizens that this whole war was a bad idea, and that they should be sensible and overthrow Hitler. Some of his more aggressive military commanders advocated more concrete action, like bombing German munition factories, but Chamberlain nixed the idea on the grounds that German munition factories were private property and that bombing them would therefore be inappropriate.
Assuming for the sake of argument, however, that the British and the French had sent some sort of token expeditionary force (it’s hard to imagine them sending a substantial force, logistically or politically) to Finland to participate in the Winter War against the Soviets, we come up against the question of how Stalin would have responded. I can’t imagine Stalin contacting Hitler – his ideological foe – and basically saying to him, “The French and the British have sent troops to help the Finns and my army can’t handle them. Can you please help us deal with them?” I think a more likely reaction by Stalin to an Anglo-French expeditionary force would have been the same one that a senior German officer (I think it was Hindenburg) had during WWI when he was asked what he would do if the British (as they contemplated doing, and as the tried on a small scale at Zeebrugge) if the British landed troops by sea on the coast of Belgium or Germany: he answered that he’d send the police to arrest them.
