According to the Royal Household:
Each year, The Queen and The Duke of Edinburgh send around 750 Christmas Cards…
All members of The Royal Household will receive Christmas presents from The Queen, and Her Majesty will personally hand out presents to some members of The Royal Household at Buckingham Palace and at Windsor Castle.
The Queen also gives Christmas puddings to her staff. About 1500 Christmas puddings…are distributed to staff throughout the Palaces, staff in the Court Post Office and Palace police. Each pudding is accompanied by a greeting card from The Queen and The Duke of Edinburgh.
To read the entire article from the Royal Household, please click here.