Prince Andrew, 60, was spotted riding horseback with a member of his stable staff after arriving at the Berkshire residence in his Range Rover wearing a facemask on Wednesday.
The Queen's second son lives nearby at Royal Lodge, a Grade-II listed property in Windsor Great Park with his ex-wife, Sarah, Duchess of York.
WATCH: Sarah Ferguson reveals unseen glimpse inside home with Prince Andrew
Speaking exclusively to HELLO! on 25 September, the day the announcement was made, Sarah said: "Soon to be Grandpa and Granny are absolutely overjoyed."
Eugenie and her husband Jack Brooksbank's first child is due to arrive in early 2021 and will be the Queen and the Duke of Edinburgh's ninth great-grandchild.
Andrew was spotted horse riding in the grounds of Windsor Castle
The Duke of York has kept a low profile since he stepped back from public life towards the end of last year.
The decision was made in November 2019, following his TV interview with BBC Newsnight, which focused on his connections to convicted sex offender Jeffrey Epstein.
Andrew was pictured driving to Windsor Castle
Andrew issued a statement at the time, saying: "I have asked Her Majesty if I may step back from public duties for the foreseeable future, and she has given her permission. I continue to unequivocally regret my ill-judged association with Jeffrey Epstein.
"His suicide has left many unanswered questions, particularly for his victims, and I deeply sympathise with everyone who has been affected and wants some form of closure. I can only hope that, in time, they will be able to rebuild their lives. Of course, I am willing to help any appropriate law enforcement agency with their investigations, if required."
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