Katherine Schwarzenegger’s daughter Lyla is not even one years old yet, but TheGift of Forgiveness author can tell that her baby girl’s “love for animals has already started.” In PEOPLE’s 2021 Beautiful Issue, the mom of one revealed that she’s already introduced her daughter to the horse that her parents Maria Shriver and Arnold Schwarzenegger surprised her with when she was 13.

“Introducing Lyla to Cinco was so fun,” she said. “I’ve had Cinco in my life since I was in middle school, so to be around him now with my daughter made me so happy. Then to be able to have her pet Cinco’s nose and get so excited about it made my heart swell!”

For Katherine, it’s “really important” to “have the barn be a part” of now her daughter’s life. “It was such a big and important part of my life,” she shared. “Growing up in Los Angeles, I think it’s important for people, especially kids, to have a place to get dirty, be free and be around animals in open spaces. It was a huge help for me growing up, and I know it will be for her too.”

Katherine, 31, and her husband Chris Pratt, whom she wed in 2019, welcomed Lyla last August. During a recent appearance on the Today show, Katherine explained why she doesn’t share photos of her daughter’s face on social media. “I think one of the greatest gifts that my parents ever gave me and my siblings is the gift of privacy and having a really normal upbringing, or as normal of an upbringing as possible,” she said. “We had a really normal and magical childhood, and we were allowed to kind of be our own people and have our own identity and kind of choose to step into whatever form of being public we wanted to when we felt comfortable. And I think that was such an incredible gift to have given us kids.”

“It’s something that is really important to my husband and I to be able to give to our kids and to be able to have that privacy, and not necessarily show as much of them on social media,” Katherine continued. “All four of us kids would say that it has been such an amazing thing that our parents gave us, and so I want to be able to give that to our baby, too.”