The answer is going to depend on the country. There is no worldwide answer.
National meteorological institutes often have maps of snow frequency. Not that you want snowcover, which may be harder to find than snowfall. Some places get lots of snowfall that melts within days, whereas others might get only little snowfall, but are so cold that any snow falling October or later is sure to remain until April at least. Interpreting precipitation + temperature statistics to estimate snowcover frequency is possible but error-prone. The answers, per country, below, are all based on snowcover data.
For example, this map shows the probability of a "white christmas" (at least 5 cm of snow on 24, 25, 26 December) in Sweden:
Frequency of White Christmas, 1931-1980. Source: SMHI
You can safely extrapolate from the gradient in this map that anywhere further south, you can't be sure to see snow (except in the mountains).
Similarly, you can browse senorge.no to get historical snow observations, although I don't know if they have a frequency map like the Swedish do.
Finnish FMI has a set of maps with snow statistics, as well as White Christmas probabilities:
Frequency of White Christmas, Source: FMI
I don't know about maps for Canada. I'm quite sure that on a map covering all of Canada, all will have close to 100% probability of snowcover in winter. Results for deep snow (say >30 cm) might be more interesting. However, Canadian Climate Normals can give you snow frequency per month for any weather station. For example, in January, Toronto has on average 21 days with >1 cm snow per year, Winnipeg has 31, Victoria only has 3.2, and St. Johns has 27.