Beatrice also borrowed the tiara that the queen wore on her wedding day in 1947.
U.S. attorney Geoffrey S. Berman, issued a statement saying the prince had tried to "falsely portray himself to the public as eager and willing to cooperate."
U.S. investigators want to interview the royal about his friendship with Epstein.
The Duke of York has declined to cooperate, U.S. Attorney Geoffrey Berman said Monday.
The Duke of York had claimed to be withdrawing from royal life over his ties to the late sex trafficker and a rape allegation.
The Duke of York relayed a message from Queen Elizabeth II at a private engagement alongside his family.
The Duchess of York has defended her ex-husband amid the allegations of rape before.
For the first time on British TV, Giuffre explains how she was trafficked by Jeffrey Epstein and forced to have sex with the royal in 2001.
Their horseback riding excursion comes days after the disgraced Duke of York said he was stepping away "from public duties for the foreseeable future."
The Duke of York announced Wednesday he is stepping away from royal duties.