There are two definitions we can use for a white Christmas - snow on Christmas Day, or snow leftover on the ground from a previous snowfall.
The last time we had a measurable snow on Christmas Day was back in 1948, when we had 0.4" of snow. (The most was 2.4" the year before, in 1947.) There have been a few years since 1948 where we had snow flurries, but they never measured up to anything more than a trace of snow.
There is a less than 5% chance of Norfolk getting a measurable snow on Christmas Day.
As for snow left on the ground from a previous snowfall, we had 4" of snow left on the ground back in 1966.