This is the second day of Winter.
Winter, meteorologically speaking is described in the Northern Hemisphere as being December, January, and February, which is, of course, a convention rather than a fact. Astronomically, winter starts with the Winter Solstice when the sun is at its lowest and so stretches from around December 21st to the Equinox around March 21st.
Logically, the solstice should be a midpoint of winter rather than the beginning of it, with 6 weeks of winter on either side of it. This is roughly what the Celtic year does, it starts at dusk on 31st October (Halloween/Samhain) and continues to the evening of 31st January (Candlemas/Imbolc). So a Celtic Winter is November, December and January.
As far as the Sun goes this is really correct, but, in fact, because of the presence of the oceans (and to a lesser extent) the earth, the coldest time is not the Solstice when the Sun is at its weakest, but a few weeks later in January. The oceans (and the landmass) retain heat, and so the coldest (and the warmest) periods are offset, so January 13th is probably the coldest day not December 21st.
December comes from the Latin for ten – meaning the tenth month. Of course it is the twelfth month because the Romans added a couple of extra months especially to confuse us. For a discussion on this look at an early blog post which explains the Roman Calendar.
In Anglo-Saxon it is ærra gēola which means the month before Yule. In Gaelic it is An Dùbhlachd – the Dark Days which is part of An Geamhrachd, meaning the winter, and the word comes from an early Celtic term for cold, from an ‘ancient linguistic source for ‘stiff and rigid’’, which describes the hard frosty earth. (see here for a description of the Gaelic Year).
My personal calendar suggests that winter begins on November 5th, because this is the day I generally notice how cold it has suddenly got. This year, my smart meter tells me that winter began in the last week of November.