What a mess our calendar is! The winter solstice would be the obvious day to celebrate the end of the year and the beginning of the new one, yet it passes with hardly anyone noticing. Instead, the pagan midwinter festival has been taken over by the Christians and moved to the 25th, with the new year starting a week after that and most activity closing down between the two. The attendant excesses of food and drink and family reunion are spread over eight days. Some people seem to like this arrangement, but many hate it. Non-Christians and people without homes or families can find it unbearable, but it is also the peak period for family breakdown.
The obvious solution would be to shift the beginning of the year and the official public holiday to coincide with the solstice, leaving the 25th for Christians. They needn't feel specially attached to that date, as no one knows when Jesus was born, and anyway Christmas is celebrated by Eastern Christians, according to the Julian Calendar, on January 7th. The giving of presents to children was imported from St Nicholas' (Santa Claus) Day, December 6th. A brutal way to make the change would be to chop eleven days out of one year, the way that Pope Gregory did. That was not popular, but a painless way to do it would be to miss out eleven leap years. Too bad for those with leap day birthdays, but they usually celebrate on the 28th anyway.
Of course, having a leap day in February is irrational; it makes the equinoxes and solstices jump to and fro. The right place for it would be at the end of the year (which is where it was when the year began on March 1st). For that matter, since we have uncoupled months from the moon, we might as well have 13 months of 28 days each; the days of the week could be absoultely regular, with every month starting on a Monday, plus an unnamed day at the end of the year (or two in a leap year). Still, calendar reform is terribly contentious, so we'd better stick with the months and leap days as they are.