My memory of the weather in Moscow was of very dry, baking hot summers (which can last well into September) and then months of freezing snow and ice (starting in late October or in November). Grey, rainy, autumnal weather wasn't much of a thing.
The only rain I particularly remember occurred during massive thunderstorms, which were not that frequent but when they did occur they were accompanied by huge downpours. These typically occured at the height of summer, not in September.
Turns out my memory corresponds with the facts: if you google the weather in Russia it says the country doesn't get a lot of rain and most of the precipitation occurs during summer thunderstorms or in the form of snow in winter. July is the wettest month.