Dickens wrote under the influence of the memory of some very bad winters at the end of what is called The Little Ice Age, in which the northern hemisphere became much colder in the 14th century and continued until the mid 19th. This was what caused the Norse settlements in Greenland to fail. There was one particularly bad winter, with deep snowfall that hung about some time, and during which some people in South Street in Lewes, Sussex, were killed by an avalanche. If you go there, look for the Snowdrop Inn, and look up at the steep slope behind it. I imagine that snow blew along the chalk down, Caburn, and formed a cornice overhanging the homes below.
Since Dicken's time, the climate has warmed, but there remains a division between North and South Britain - the north has far more regular snow than we do in the south. There has been another step up in temperature over the past few decades. There are fewer heavy falls that hang around than I remember in my younger days.

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