The tables below (figs 1 & 2) rank the mildest and coldest Christmas and New Year’s holidays since 1772. For the purposes of these statistics which I’ve generated from the daily CET values from 1772, I’ve extended the holiday to cover the period from the 21st of December to the 4th of January.
The extreme coldest Christmas and New Year occurred in 1870-71 (fig 1), in fact it’s coldest by quite a margin, although I can glean nothing about what must have been a classic Dickensian Christmas from searches on the internet. Only two such extreme cold holiday periods have occurred during this century, namely the consecutive years of 2009-10 and 2010-11, that appear in the top forty.
There are no shortages of extreme mild winters in the top forty from the 21st century though, in fact it already contains five, with 2015-16 being the warmest Christmas New Year in the last 245 years, again by a very large margin.