Being from Scotland I call New Year's Eve Hogmanay. The day is traditionally spent cleaning the house, especially the kitchen, all the fireplaces and all the windows. I remember finishing them off madly just before midnight.
Tradition has it that to ensure the family has enough money for the New Year everyone in the household puts some money outside on Hogmanay, perhaps hidden on the stoop or tucked into a planter, then on New Year's Day it could be brought back in.
Before midnight the tallest man with dark hair went outside by the back door, got a lump of black coal from the shed and came round to the front door. At midnight he would knock on the door and present it to the head of the household wishing him a warm and prosperous new year. The coal would be added to the fire and the tall man would be invited in for a dram of whisky and we'd all sing Rabbie Burn's Auld Lang Syne. Incidentaly, my Mom's sister, my Aunt Betty lived on Clochranhill Road round the corner from Rabbie Burn's cottage in Alloway.
Then the "first footing" would begin. We'd all visit each others houses, shortbread and whisky flowed and the party had begun, often lasting for a good couple of days.
Christmas Eve was the day the "tree" was put up and decorated and in ther evening it was time to go to church and give thanks for the year. Christmas Day was a family day and not nearly as important as Hogmanay. It was a working day for a lot of people and not an official holiday till 1958. Boxing Day was not a Scottish holiday. However, Hogmanay and the first of January were holidays. My dad's business closed on Christmas Eve and didn't reopen till about the 3rd or 4th of January; there was no point, as nobody would have turned up at work anyway. Hogmanay was cleaning and then partying, time to chase away the darkness of that time of year when there were so few hours of bleak daylight.
That being said, I'm in Canada now, so Happy New Year to you and yours.