Sienna Miller Says She Adopted a Bunny She Met on the Horizon Set for Her Daughter (Exclusive)

Sienna Miller's family gained a fluffy new friend from her latest film project.

Speaking with PEOPLE about Horizon: An American Saga, the actress, 42, reveals that she adopted a rabbit after her 11-year-old daughter, Marlowe, visited the movie's set.

"It was a great set to have kids on because there are animals everywhere, and everybody's in costume," Miller says of the Western epic directed by Kevin Costner.

"It is very familial, because he's a dad of many kids, and everybody's welcome," she adds. "It's a very open, gentle set."

Coster has seven children, including 15-year-old Hayes, who plays Miller's son in the film. He also shares three adult kids — Annie, 40, Lily, 37, and Joe, 36 — with his ex-wife Cindy Silva and son Liam, 26, with former partner Bridget Rooney. He shares Cayden Wyatt, 17, Hayes, and Grace Avery, 14, with ex-wife Christine Baumgartner.

Miller says the movie's director of photography, J. Michael Muro, and his wife breed rabbits, which is how she came to find her new pet.

"So on a night shoot, [Muro's wife] turns up with six baby bunnies, and it's 2 a.m., and you're just stroking a baby bunny," she recalls. "My daughter then comes to the set and hears that there are baby rabbits, so we now have a rabbit."

Miller says she "smuggled" the bunny, named Cloudy, on a plane back to New York from Utah, where she was filming Horizon.

"I pretended it was a cat," she continues. "I just hid the ears. I was like, that's my kitten."

Miller shares Marlowe, born in July 2012, with her ex Tom Sturridge. The actress and her boyfriend, Oli Green, welcomed a daughter around six months ago.

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Costner, 69, opened up about working with Miller in an interview with PEOPLE this week, revealing that Miller had a note for him about directing his teenage son.

"She's our leading lady. She's incredible in the movie," he said. "And she came to me one time, she says, 'You're kind of hard on Hayes,'" Costner said. "And I said, 'I know. I need him to be really good, and he's inexperienced, and I'm going to help him all the way through.'"

"And in the end, Hayes started doing some things on his own that were just magical, and I'm really proud of his performance," Costner added.