Hobbits had a calendar of their own, called 'Shire Reckoning.' It was adapted from the King's Reckoning of the Dunedain, which in turn copied that of the Eldar. The hobbits made several contributions of their own to time-keeping. Having exact and orderly dates was important to them because of their interest in genealogies.
Their year is the same length as ours, having 365 days, and one leap year of 366 days every fourth year. The year was divided into twelve months of thirty days each. The names of these months were Afteryule, Solmath, Rethe, Astron, Thrimidge, Forelithe, Afterlithe, Wedmath, Halimath, Winterfilth, Blotmath, and Foreyule. There also were three additional Lithedays and two Yuledays. The first day of the year was called 1 Yule, and always occurred on the first day of the week. The last day of the year was called 2 Yule, and always landed on the last day of the week. Mid-summer's Day was the summer solstice, resulting in their year being ten days ahead of ours. 1 Lithe was the day before and 2 Lithe the day after Mid-summer's Day. In leap years, a fourth Litheday, called Overlithe, was placed between Mid-summer's Day and 2 Lithe. This quadrennial holiday was a time for feasting and celebration.
Each week had seven days, starting on Saturday and ending on Friday. However, the hobbits had different names for the days. They were adapted from Dunedain, and archaically were Sterrendei, Sunnendei, Monendei, Trewesdei, Hevenesdei, Meresdei, and Highdei. At the time of the War of the Ring, the names had changed to Sterday, Sunday, Monday, Trewsday, Hevensday, Mersday, and Highday. In the reign of Isengrim II, the Shire-folk introduced a small innovation they called the Shire-reform. Mid-summer's Day, and on leap years, Overlithe, did not belong to any week, ensuring that dates always landed on the same day of the week. Another result is that Highday, or Friday, never landed on the first day of the month. There was a jesting idiom popular among the Shire-folk that ran 'on Friday the first of Summerfilth.' This was the day on which unlikely events were to occur, such as pigs flying. Of course, this never came.
Shire Reckoning began in year 1601 of the Third Age. It continued on it own pace until the Fourth Age, SR 1422, and continued still, until this very day.
All this accounted for, Tuesday, December 25, which happens to be today, would be, in Shire Reckoning, Trewsday, Afteryule 3. Merry Christmas!
Part II: Concerning Etymology
Tolkein, J.R.R. The Hobbit UK: George Allen & Unwin, 1937
Tolkein, J.R.R. The Lord of the Rings UK: George Allen & Unwin, 1954-1955