score:6
The best time to visit is around Easter, when there's lots of snow, it's not too cold and there's sunlight, but October is a reasonable option.
Snowfall: Statistically, the "first snow" (ensilumi), meaning uninterrupted snow cover, falls around the 2nd week of October. However, this is highly variable and there's a real chance of slush or rain, especially towards the beginning of the month.
Aurora: Statistically, October is the third best month for spotting auroras in northern Finland, behind only Jan/Feb. (Rovaniemi is about halfway between Ivalo=I and Oulu=O in this graph.)
Sunlight: Days are "normal", meaning from 9 AM to 5 PM. (In December, you get the polar night, meaning no sun at all, for a few days.)