The card was in response to well-wishers' Christmas messages.
The walk was on the Sandringham estate, where the royal family traditionally spends Christmas.
Last Christmas was the first without Queen Elizabeth, who passed away in September.
Plans are in motion for the royal children's participation in the coronation of King Charles and Queen Camilla on May 6.
Prince George may have a role in the service, but it hasn't been officially confirmed.
William and Kate are aware that George is old enough to understand what is going on.
Normal life resumes when George is back at school with his classmates.