After the polnish army had been effectively gone.
Also, not even the purge explains the errors done by the big guys including Stalin during the first days - Most losses of the USSR happened during the first few weeks of the war and had been extremely grave. Still people had been pushed with the wrong equipment into the wrong war. The Soviets entered Finland with green helmets and green uniforms - and never changed it.
Well, first and most serious mistake made by Soviets was underestimation of the Finnish fighting potential. But I should say everyone else underestimated Finns too, and it was one of the factors forced Germans to believe Red Army is weak and easy to defeat since it was unable to crush even this small country.
You have to take into account that Red Army never had a serious combat experience before (Civil War was just a bloody massacre). Winter combat, submachine guns, snipers, wide use of minefields - all these factrors were new for unexperienced Red Army commanders. Everyone who was able to take right decisions about it was already in jail or in grave because of previous purge, so acting commanders had to learn it hard way.
Green uniform on snow wasn't the most stupid thing on this war. In my opinion the worst was using the chain fighting formation against machinegun bunkers. I've heard reports about Finn machinegunners getting insane because of the amount of people they've killed and, most of all, because they kept coming over and over again.
Have in mind too that Soviets won this war, even thought it was a Pyrrhic victory.
