Halley offers no clues in either of his logbooks as to how he spent Christmas; he’s anchored in Rio during Christmas on his second voyage and for all we know he and his crew could be having a beach barbecue and dancing the samba!
However, we do have some idea of how a ship’s crew celebrated Christmas Day in the late seventeenth century from the highly entertaining Diary of Henry Teonge, which provides two accounts of Christmas spent on board a ship. 
Henry Teonge (1621-1690) was a Warwickshire clergyman with a wife and four children, who, probably owing to poverty and debts, went to sea as a Royal Navy chaplain in his mid-50s.
On his first voyage, Henry was entered as chaplain on board the fourth-rate frigate Assistance on 27 May 1675, under the command of Captain William Houlding; on his second, he served on board the Bristol under Captain Anthony Langston, transferring mid-voyage with his captain to the Royal Oak. He kept a diary of both voyages (May 1675-Nov 1676 and May 1678-Jun 1679) and it seems fair to say that the ageing Henry proved a natural-born seaman.
He was interested in all aspects of life aboard the ship and in the places he visited, but his main interest – sensible man! – was his belly, and his diary has numerous, highly-detailed reports of meals, including those he enjoyed on Christmas Day.
His first such entry was for Christmas 1675:
Chrismas day wee keepe thus. At 4 in the morning our trumpeters all doe flatt their trumpetts, and begin at our Captain’s cabin, and thence to all the officers’ and gentlemen’s cabins; playing a levite at each cabine doore, and bidding good morrow, wishing a merry Chrismas. After they goe to their station, viz. on the poope, and sound 3 levitts in honour of the morning. At 10 wee goe to prayers and sermon; text, Zacc. ix. 9. Our Captaine had all his officers and gentlemen to dinner with him, where wee had excellent good fayre: a ribb of beife, plumb-puddings, minct pyes, &c. and plenty of good wines of severall sorts; dranke healths to the King, to our wives and friends; and ended the day with much civill myrth.
Not bad, but his second Christmas dinner (1678) seems to have been even better, though not apparently as good as they’d actually planned:
Good Chrismas Day. Wee goe to prayers at 10; and the wind roase of such a sudden, that I was forced (by Captain’s command) to conclude abruptly at the end of the Letany; and wee had no sermon. And soone after, by the carelessnes of som[e], our barge at starne [stern] was almost sunk, but recovered. Wee had not so greate a dinner as was intended, for the whole fleete being in this harbour, beife could not be gott. yet wee had to dinner, an excellent rice pudding in a greate charger, a speciall peice of Martinmas English beife, and a neat’s tounge, and good cabbige, a charger full of excellent fresh fish fryde, a douzen of wood-cocks in a pye, which cost 15d., a couple of good henns roasted, 3 sorts of cheese; and last of all, a greate charger full of blew figgs, almonds, and raysings; and wine and punch gallore, and a douzen of English pippens.
Wine and punch galore! One can’t help thinking that a Royal Navy ship was rather a good place for a destitute gourmet to spend his Christmas. But it was also a day of contrasting emotions for Henry, as his entry continues:
The wind was so high all this night, that wee ever expected when it would have broake our cable or anchor. But the greatest losse wee yet sustayned was this: about 11 or 12 a clock our honest Leiuetenant, Mr. Will. New, dyed, and left a mornfull ship’s company behind him. Yesterday our Capt. bought 3 Spanish hoggs: the ruffnes of the weather made them so sea sick, that no man could forebeare laughing to see them goe reeling and spewing about the decks.
As I said, we have no idea how Halley spent his Christmas but it seems a safe bet that the atmosphere was a lot friendlier on the second voyage than on the first, and so I hope they were as merry as Henry and his brother seamen evidently were on their voyages.
Wishing all our readers a Merry Christmas – and do go easy on those “minct pyes”!
 The Diary of Henry Teonge, Chaplain On Board His Majesty’s Ships Assistance, Bristol, and Royal Oak, Anno 1675 to 1679 (London, 1825). There is an online version here.