Christmas at Godmersham may have been overshadowed by mourning for Mrs Austen-Knight but the family may still have received visitors and a Christmas meal.
Letters and diaries of JA's family mention Christmas activities. Fanny Knight Austen described dances, gift giving, family visits, and games at Christmas; Hunt the Slipper, Snapdragon, Bullet Pudding and Apple in Water.
Ref : Maria Hubert. Jane Austen's Christmas Sutton Publishing. 1996. pp 51-53
In Persuasion, Jane Austen wrote an account of Christmas in her time.
'Immediately aurrounding Mrs Musgrove were the Litle Harvilles, whom she was was sedulously guarding from the tyranny of the two children from the Cottage, expressly arrived to amuse them. On one side of the table, occupied occupied by some chattering girls, cutting up silk and gold paper; and on the other were tressels and trays, bending under the weight of brawn and cold pies, where riotious boys were holding high revel; the whole completed by a roaring Christmas fire, which seemed determined to be heard...Charles and Mary also came in, of course, during their visit; and Mr Musgrove made a point of paying his respects to Lady Russell and sat down close to her for ten minutes, talking with a very raised voice, but, from the clamour of the children on his knees, generally in vain. I t was a fine family-piece.
..."I hope I shall remember, in future," said Lady Russell as soon as they were re-seated in the carriage, [to Anne] "not to call on the Musgroves in the Christmas holidays".
Persuasion, Ch. 14
You can also check the L&T archives for many posts on Christmas in Jane Austen's time. JulieW included picutes in her Christmas posts showing how great houses like Godmersham celebrated Christmas- with evergreens of holly decorating the mantlepiece, mistletoe,tables laden with pies and the Christmas custom of the Twelveth day cake.
D. Le Fay in her biography of Jane Austen mentions at Christmas 1782, when Jane was seven her brothers put on a play, a tragegdedy called Matilda and mentions the presence of friendly neighbors- the Digweeds, Portals,Terrys and Lyfords who were invited to the performance in the Austen barn. pp.32-33.
Although Christmas wasn't the same in post-Georigian times; but the Christmas season appears to be a time of family gatherings, visits with games, home theatricals, balls and gifts for children. :)