I do rate this highly, more than just the typical advance of snow across Russia/Siberia through October.
If we take a look at snowfall across Russia and Scandinavia in the Octobers preceding the colder winters we've had since 2009, there is definitely a trend there regarding Scandinavian snow cover and the weather we experience. For this post I will focus on snow cover charts from 10th October each year, posting three charts dated 10th, 20th, and 31st October to see the extent of snow cover in Scandinavia. Although I said I rate this more highly than the typical advance of snow across Siberia, a RAPID advance coinciding with snow cover in Scandinavia does seem to occur in my opinion (although do correct me if you think otherwise!!). This will also be detailed.
1) October 2009
By this date in 2009 we had a decent amount of snow in Scandi, which stayed put ten days later. This was arguably followed by a rapid advance of snow towards W Russia up to the end of the month that year. Tick?
2) October 2010
10th October had zero(!) snow in Scandinavia, but patches began to appear a few days later. There was no rapid advance in 2010, but snow did appear and stick around above 60N as did the snow in Scandi albeit less impressive than 2009. Tick? A less convincing one maybe but still scope for agreement.
3) October 2012
10th October 2012 again had zero snow in Scandi, away from higher parts of Norway that is, but some did appear before the 20th. Then by the end of the month, we had seen possibly one of the fastest advances of snow on record through Russia and almost all of Scandi too. Another less convincing tick for Scandi but a huge tick for rapid advance.
These three genuine cold winters did share common factors of rapid advance of snow cover, at least some snow in Scandi, or a slight combination of both. There are exceptions to the rule of course as October 2013 had similar outcomes but we know what happened that winter! This is also far from an exact science as we know, but there is definitely some sort of link with colder winters here to my untrained amateur eye. Things like la nina, QBO, etc have their own effect in varying capacities in different winters, so it's hard to give definitive answers...