Not sure when you are talking about but we haven't played later than Dec 23rd since 1992. Personally I would ban games on Xmas Eve and NYE due to all the problems it causes, as SoS list above, but given we played on NYE last year....
Used to play back to back games on Christmas Day and Boxing Day at one time. So we'd have been away to Arsenal Christmas Day, then play them at home on Boxing Day.
If Christmas Eve was a Saturday, then they'd play three days in a row. Everton got over 200,000 once over a Christmas weekend.
It'll have been a long time since we'd have played Christmas Eve because we still traditionally play Boxing Day, and todays players can't cope with two matches in three days.
I still remember they're being a full football fixture list if Christmas Eve was a Saturday. I think in Scotland they still play Christmas Eve.
The only reason not to go to a match on Christmas Eve is if you've got kids. That'd rule out 90% of our current home support, but at one time it'd be an end full of teenagers with nothing else to do (before they go out on the piss).