"Old Christmas," in England and Ireland, was a name for January 6, coinciding with Twelfth Night, the Epiphany. The tradition continues in the maritime provinces of Canada and Appalachian America—and perhaps in parts of the British Isles as well. Bloom and Josie (and Molly, too) have been at a party on Jan. 6, 1888.
A post on the Archival Moments website from St. John's, Newfoundland explains the origins of the phrase: "The season of Christmas in Newfoundland and Labrador ends on “Old Christmas Day,” January 6th also known as “Twelfth Day.” The name “Old Christmas” stems from a piece of legislation introduced before the Parliament in London, England called the Calendar Act of 1751 that came into effect in 1752. Before the calendar was reformed, England celebrated Christmas on January 6th. Essentially what happened in 1752 was that twelve days were dropped from the then existing (Julian) calendar that was used in England and Ireland and the new Gregorian calendar (instituted by Pope Gregory XIII), was adopted. In 1752 purists said that the “real” Christmas Day was not on December 25th, but January 6th, 365 days after the previous Christmas. In centuries past, Christmas was deemed to start at sunset on Dec 24 and so the 12th night following it was Jan 5. Nowadays, people count from Dec 25 and so assume Twelfth Night falls on the 6th" (http://archivalmoments.ca/2012/01/old-christmas-day-trees-cakes-and-cows).
Another website, Amish America, offers additional information: "From the Pinecraft Pauper: January 6th is still widely observed as a holiday by many plain folks, who commemorate the Epiphany with rest and fasting. The Epiphany, traditionally, is the day in which the wise men brought gifts to Jesus. However, January 6th is called 'Old Christmas' because in 1582 Pope Gregory XIII deleted ten days, eleven minutes, and fifteen seconds from the calendar, to realign it with the seasons of the year, thus technically moving Christmas from Dec. 25th to Jan. 6th. The Scotch-Irish Mountain folks up in Tennessee still call the 6th 'Old Christmas.' Their tradition has it that one ought never lend anything to anybody on that day, for the lender will never get it back." The site also gives the broader history of the calendar change: "Calendar reform was implemented at different times in different countries in the centuries following the Pope’s decree. Four countries implemented the change on the intended date. In Spain, Italy, Portugal, and the Polish-Lithuanian Commonwealth, October 4, 1582 was followed by October 15, 1582. As the years went on, time due to the miscalculation in the previous Julian calendar accumulated. This meant countries who adopted it later had to make a change of more days. When Britain (and the American colonies) adopted the calendar in 1752, it was necessary to add 11 days" (http://amishamerica.com/amish-celebrate-old-christmas).