Apparently, according to Celtic/Gaelic calendar, it's already winter, since November (Samhain) is the first winter month. It does make sense from the point of view of the days getting extremely short and the general darkness of the season. For about a week already it's been getting dark at around 4 p.m. over here, and even earlier, though today the sun came out and the temperatures are more suitable for spring than for winter.
Samhain was also the name of the precursor of the modern Halloween and it was an important pagan festival, marking the end of the harvest season, as you probably know. It's interesting that in The Hobbit Tolkien mentions something about the old dwarves' calendar where the New Year began in November, so you can see where he got it from.
In ancient Rome, on the other hand, the year originally began in March (September = the seventh month, October = the eighth month, November = the ninth month with December being the last, tenth month and the winter days originally not belonging to any month at all). In the times of Julius Caesar it did already begin in January. Caesar further reformed the calendar, by, among other things, adding ten additional days and thus making the official year 365 days long.
He also apparently changed the length of the week, as in the times of the Republic Romans still were using the original Etruscan system of the 8-day week with one designated market day.
It's interesting that in different countries the year began on a different day. 1 November by the Celts, 1 September in Byzantine Empire, 25 December in Anglo-Saxon England and yet since Julian Calendar became the official calendar of the Roman Catholic Church all the other calendars became eventually aligned with it, (and later with Gregorian calendar) so that the first of January officially became the New Year's Day.
The Ancient Roman civilisation is long gone, but its legacy still survives. Definitely something to think about.