Probably 5 B.C. according to most historians.

Nobody really knows the month but probably not December. Mid-Winter would have been an unlikely time to hold census.  When Christianity spread north, Christmas replaced the existing Winter Solstice festival.

You would have been running low on hay to feed your cattle by now, so you might as well slaughter a lot of them and hold a feast. Anyway, you need something to cheer you up at this time of year!