Xmas Day
I think you will find the airport has been open on Christmas Day for a few years now, I think Monarch and Thomson usually have a flight and not sure if El Al will have one also this year. A number of executive flights are operated as practically all other business airports e.g. Farnborough, Biggin, etc are closed.
Regarding the snow problem - can we get some reality here, Luton Airport is over 500 ft agl so it is bound to get its fair share of snow. The problem is that the United Kingdom over the last 20-30 years has got itself into a sense of false security regarding winter weather. The country is in Northern Europe it is winter and surprise, surprise it gets cold, sometimes snows, has ice and fog. If people of my age remember this was a regular occurrence way back in the 1950-60s you expected it to be cold and snowy during the December-March period. You just got on with it - and do not get me on that global warming rubbish!