Somehow Stalin is convinced not to be paranoid for a few months and just let Finland be. Given that the main reason that the Finns sided with Germany later was revenge/get back their stuff they probably don't in this TL. How badly does this hurt the Germans?
Probable effects I can see:
1) Germans less contemptuous of Soviet Army
2) Soviets don't learn tactics like ski troops from Finns.
3) Soviets don't realize how bad their leadership is
4) Lots of Soviet soldiers still alive.
5) Of course no need to fight over territory north of Leningrad, meaning more troops for the other fronts
Why exactly would Stalin just "leave Finland be"? Getting free hands for the USSR in terms of Finland and the Baltic states was one of the main benefits of the Molotov-Ribbentrop Pact from Stalin's POV. Taking these areas "under the Soviet protection" would safeguard the USSR against them being used as a springboard for an invasion, and then Stalin seems to have had an interest in retaking the borders of the Russian Empire for the USSR. The war in the West provided an apparent smokescreen for Stalin to pursue his goals along the Soviet Western borders. He considered all these four nations military pushovers, and this was in the event true of the Baltic states. Stalin could not apparently foresee Finland being able to put up the fight and at the time, for example, also Mannerheim thought Finland could not last for more than two weeks in a war alone against the Red Army.
So, to prevent the Winter War, you would have to convince Stalin that attacking Finland would cause more trouble than he expected. That is a pretty tall order, under the circumstances. Stalin thought it would be a cakewalk, just the matter of kicking in the door and watching bourgeois Finland collapse on itself. I personally think that without significant PODs prior to late summer 1939, the best realistic way to avoid the Winter War as it was would be for Finland to cave in to Soviet territorial demands in the fall of 1939.
This would depend on Finnish opinion of the German invasion and their relations with both sides. if the Germans influence the Finns enough, people like Ryti and Mannerheim could become supporters of the german cause, promised big chunks of land. Some think the Finns got their eye on Karelia, even without the territory losses of the winter war. Next to that, President Ryti had fantasies about a greater finland, and believed in German victory over the Soviet Union. They were quite nationalistic i think.
If they indeed don't though, this frees up forces for the Germans as well. Operations for army group North would probably be harder since the Soviets got more troops to spare, but not as much as you might think since the Soviets still got to protect the borders with Finland in case of a possible Finnish attack. However once winter arrives the Soviets are less prepared as well, less experience. However the siege of Leningrad will be a lot harder as well.
Its a balance of power you can only guess at.
If there is no Soviet aggression against Finland in 1939-1940 and if by some magic also Soviet territorial demands on Finland are avoided, the Finnish leadership would do all in its power to keep Finland neutral and outside the war. The Winter War and the USSR's proven hostility to the very idea of the existence of an independent Finland were very significant in pushing Finland into Germany's arms. There is a small chance that political and economic isolation would push Finland into a grudging sort-of alliance with Germany anyway by 1941, out of necessity, but even in that case the greed for Eastern Karelian clay wouldn't be the deciding factor behind this move - keeping the Finnish people alive and fed would be. IOTL, the perceived need to protect Finland from a renewed Soviet attack and the need to have secure lines of supply, lest Finland be visited by famine, were the real reasons for the German alliance. That the alliance allowed potential territorial expansion was an afterthought. Both Mannerheim and Ryti were Anglophiles by inclination. Ryti was a moderate liberal, a lawyer and a banker who had studied in Britain (and been honoured as a Knight Commander of the Royal Victorian Order by George V in 1934 for his work to improve Finno-British connections). He was not known as anything like an irredentist nationalist before the war. In a situation where Finland seems to be under no real threat from Soviet attack and where Finland's food security and trade connections are secure, they would not ally the nation with Germany just because of designs of conquering Soviet Karelia. Then there is of course the fact that avoiding the Winter War could well butterfly Ryti's ascension to prime minister and thus avoid his presidency as well.
