Scotland did have a "Cake Day" on New Year's, so take that for what it's worth.
26 December 2004, New York Times, city section, pg. 2:
Q. I came across a reference to "Cake Day" as a traditional holiday in old New York, and grew curious. It sounds like a child's birthday party.
A. The holiday was New Year's Day, and the cakes are explained in a 2002 article by Sibyl McCormac Groff in Antiques magazine.
Until the late 19th century, New Year's Day was celebrated more widely than Christmas in the city. "One of the holiday customs continued by New Yorkers was the longstanding Dutch tradition known as New Year's Day calling," Ms. Groff wrote.
Every woman who considered herself anybody stayed at home, dressed in her best, beside a table covered with cakes, preserves, wines, oysters and coffee. The number of callers was a source of pride and competition.
"For the gentlemen," Ms. Groff wrote, "New Year's Day calling, or 'cake day,' as it was sometimes called, was a race to see how many calls one could make to the houses of friends and associates." One mayor made calls for five hours while his daughter entertained 169 well-wishers. Instructions for the feast and the day's etiquette were printed in contemporary magazines. The tradition died as neighborhoods fanned out, making calling impractical.
6 January 1941, New York Times, pg. E8:
At noon on Dec. 31 workers in Scottish shipyards and engineering works to the number of a million or more laid down their tools and began a brief holiday. It is curious to find old folk-custom prevailing even in a period of extreme national danger. Hogmanay, said to be a Norman word, is the name given in Scotland and to some extent in Yorkshire to the last day of the year, more popularly known in the Land of Cakes as Cake Day.
What Christmas Eve and Christmas and Boxing Day are to South Britain, the last day of the year, New Year's Eve and Day are, or at least long were, to Scotland. In the old convivial times the New Year festivities were called Daft (mad) Days. On Hogmanay, children, especially in the country and in remote places, used to wrap themselves up in a sheet doubled in front to make a pocket and visit the houses of the well-to-do, where they cried "Hogmanay!"
To them this meant a quarter of an oat cake, with sometimes a bit of cheese for favorites of a particular household. Such begging rites, fragments of forgotten memories, survive in almost every country. The Scots workmen out for a lark may have forgotten or never heard of the old custom, so many of them are city-born. They have not forgotten a memorable feast day of the Scots Calendar. On Hogmanay the boys called "guisers" (maskers) used to sing or present a sort of rough drama. Sir Walter Scott always had this played by guisers art Abbotsford. If Hogmanay did nothing but remind us of that brave spirit it would be worth remembering.