Actually November is not the coldest month. Yeah it will be colder than SG, but no where is it the coldest month of the year. That's typically January.
The likelihood of snow in November is low, but the weather in temperate countries can be unpredictable; just has how it can rain in Singapore any day of the year. December was the coldest winter we had in 100 years in the UK, and it was similar in France. Some parts of England had snow starting from early December, and perhaps even late November. We had about 10 - 20 cm of snow that came in mid December and stayed all the way till past Christmas, giving us a beautiful White Christmas, which is fairly rare in the UK.
So while it's unlikely, I won't wager my house on it.
Are you looking for snow or you are NOT looking for snow? If it's the former, you should just head to the French Alps or the Pyrenees.