At Christmastime outright pirates and buccaneers participated in the usual carousing. They celebrated at sea and on shore, sometimes for days. Barrels of wine, liquor, and their limited fresh food were brought out. During the festivities they might have their first taste of meat for the first time in weeks. Pirates kept livestock on board their ships when they could, so it wasn't unusual for a pig to be killed for the Christmas feast. Buccaneer Basil Ringrose recalled that in addition to a large hog, "we bought a Spaniel-Dogg of the Quarter-Master for forty pieces of Eight, and killed him; so with the Hogg and the Dogg, we made a Feast, and we had some Wine left, which made us merry".
Christmas on shore could mean even better meals of fresh beef, goose, chicken, rice, even fruit.
For other pirates however, Christmas was more solemn. French Catholic pirates sometimes took mass unbelievably seriously:
"...the pirates asked the curé to say Mass on their barque, and he was unable to refuse this request. They sent for the church ornaments, and put up and alter on the poop under and awning, and then chanted Mass lustily.
A salvo of eight cannons marked the commencement of the service, they fired a second salvo at the Sanctus, and third at the Elevation, a fourth at the Benediction, and lastly a fifth after the Exaudiat, while the prayer for the King was followed by the most hearty 'Vive le Roi'.
Only one incident slightly marred this ceremony. One of the pirates adopted an offensive attitude during the Elevation, and on being rebuked by the captain, he replied insolently with a horrible oath. [French pirate Captain] Daniel promptly drew his pistol and shot him through the head and swore by God that he would do the same to anyone else who showed disrespect to the 'Sainte Sacrifice'."
Not all Christmas celebrations were quite so grand. If there were no fresh provisions, pirates might be forced to eat meager rations of pickled salt beef. Naturally the officers on board got first choice.
As for New Year's Day, there doesn't appear to be nearly as many references to it as Christmas. Woodes Rogers mentioned it briefly, though Rogers would probably have been outraged at being labelled a pirate. Nevertheless, Rogers the privateer, and later the first Governor of the Bahamas noted:
"This being New Year's Day, every officer was wished a merry New Year by our music; and I had a large tub of punch hot upon the quarterdeck, where every man in the ship had above a pint to his share, and drank our owners and friends healths in Great Britain, to a happy new year, a good voyage, and a safe return. We bore down to our consort and gave them three Huzza's, wishing them the like."
A Buccaneer's Atlas by Basil Ringrose
A Cruising Voyage Round the World by Captain Woodes Rogers
Christmas Holidays at Sea in the Golden Age of Piracy
A General History of the Robberies and Murders of the most notorious Pyrates by Captain Charles Johnson
A New Voyage Round the World by Captain William Dampier
The Sea Rover's Practice: Pirate Tactics and Techniques, 1630-1730 by Benerson Little