Hi
I went on this trip in October last year and although it wasn't too cold, it was wet and windy a lot of the time. I think in September you may have a better chance of some sun but you do spend a lot of time on this trip inside. Museums, coach, on the train etc. The real free time to explore is in St Petersburg which is beautiful and we were lucky with the weather here altho it was still quite windy at times.
Hope you have as wonderful time as I did whichever date you choose.