The Duke of York, 65, donned a long brown coat, and riding boots for a trot around the Berkshire estate on the same day that King Charles will mark Commonwealth Day in the UK.
The statue, in Northbrook Street, Newbury, Berkshire, was damaged before the broken piece was stolen shortly after 2am on Sunday, Thames Valley Police said.
A sculpture of the character written about by Michael Bond and featuring in a trilogy of hit films had been unveiled in the author's home town of Newbury, Berkshire.
The Duke of York, 65, and a groom laughed together as they travelled around the Berkshire estate on horseback, as they typically do every Saturday morning.