But his childhood prior to that was characterised by 8 consecutive white Christmases.
Dickens was born on the south coast but here is the weather for Christmases in London
1812: cold, frost, snow from a previous fall may have lingered
1813: mild and drizzly
1814: some snow
1815: cold but dry, a frost
1816: fine but average temperatures
1817: snow grains
1818: foggy with rime
1819: hoar frosts, fair
1820: cold cloudy, bleak but no mention of snow
1821: fine
1822: cloudy and fine but cold
Definitely some cold Christmas in that early period but they appear to be the anticyclonic type. Nowhere does it say an appreciable snowfall fell on the big day.
Going off this evidence and what happened before and after the big day, I suspect that Dickens experienced a run of snowy White Christmases is a myth during his youth.
MANCHESTER SUMMER INDEX for 2021: 238
Timelapses, old weather forecasts and natural phenomena videos can be seen on this site
http://www.youtube.com/channel/UCgrSD1BwFz2feWDTydhpEhQ/playlists