Given the USSR never intended to honour the agreement with Germany in long term, the terms assigning Finland to German sphere are highly improbable. Placing an eventually hostile entity in artillery range (32km) of second-largest city and the main port of state (Leningrad) is the strategic madness.
As about PODs giving Finns greater awareness, it is also meaningless. The Finnish civil war events, and later tensions about periodic Soviet incursions inter-war were already well understood as the prelude for the eventual war.
What Finnish people may benefit is large-scale export-oriented arms company similar to Swedish Bofors. Such company provide both direct military and political/diplomatic benefits. In general, because understanding of threat environment was better in Finland compared to say Poland, the Finland may even replicate the fate of Sweden or Swiss - avoid invasion altogether. I do not know why the business opportunity was not implemented IOTL though.
It could be possible that Germany secretly arms the Finns behind the Soviet's back in order to destabilize and weaken the USSR when Germany strikes east. Also, by using Finland as an experiment, Germany can see the capabilities of Russia and make them lose prestige and face.
I believe Germany did, in fact, approach the Finns during the Winter War with several offers that involved weapons shipment, but were rejected by the Finnish government.
Delay the war until the Spring of 1940. The thaw will turn much of Southern Finland into a giant marsh, while logistic constraints (Artillery and Anti-Tank production was not geared up in time IOTL) as well as new equipment (Namely Western planes and more volunteers, for example) will arrive.
The good part of the war starting in the winter was that many Soviets froze in the harsh winter, though tanks would be neutralized if the Soviet offensive happened during summer (when lakes, ponds, and swamps weren't frozen over, which easily allowed tanks and armored vehicles to advance).
Finland was very reluctant to use foreign volunteers in combat due inevitable diplomatic problems. Positions of Finland were too weak to risk renouncing some trade/peace treaties with Western states by utilizing mostly pro-Axis volunteers, and opposite way too. As about starting war in mud season, this is clearly ASB. Soviets planners were miscalculating, but were not the stone-age cave cave dwellers.
But if the situation came to the point where Finland could potentially hold the Soviets with few divisions, wouldn't Finland not be as reluctant to use volunteers? After all, the men were volunteers.
Is there any possible PoD where the Soviets advance in the spring or summer? Perhaps have it so that Stalin listens to his planners and allows them to prepare the logistics to invade Finland, thus delaying the invasion by a few months?