Jared Padalecki on the Sweet (and Unique) Musical Bedtime Tradition He Has with His Daughter, 3½

Jared Padalecki's daughter Odette Elliott, 3½, has a preference for a very specific (and unconventional) lullaby.

In a conversation with PEOPLE for this week's issue, out now, the Walker star, 38, says that he always comes equipped with a new offering for his little girl when it's time for her to go to sleep, as she "always wants a bedtime song or story."

"Last night I made up a song about a coyote chasing cats," Padalecki shares. "Your 3-year-old asks for a song about a coyote, you just do it."

After being on Supernatural for 15 years, the father of three (he and wife Genevieve also shares sons Austin Shepherd, 7, and Thomas Colton, 8½) admits he's happy to embrace his "homebody" nature.

"During Supernatural, there were some months where I would only see my family for three or four days. That's the reason Jensen [Ackles, his costar] and I wanted to bid a fond farewell to it," Padalecki says.

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He adds, "We both have wives and three kids and wanted to meet them."

Padalecki is also excited for his children to see his new show, which is a reboot of Walker, Texas Ranger, the 1993-2001 show starring Chuck Norris.

"For 15 years, I worked on a show that I didn't really want my kids to watch because I'd have to explain why Daddy was bleeding, and why Daddy was killing Mommy or why Uncle Jensen killed Mommy," he tells PEOPLE.

"They were having nightmares, and so the idea that I could let them watch this new show is pretty special," Padalecki adds.

And when he and his family are traveling, Padalecki always comes prepared — even if it might mean a little bit of overkill to some.

"My wife, Genevieve, and I took our kids on a road trip to Yellowstone, so I went to a survival store and bought three or four bear sprays and attached them to my belt," he says.

"She was like, 'You look like an idiot,' " adds Padalecki, admitting he's "terrified" of the mammals. "But you never know."

Walker airs Thursdays at 8 p.m. ET on The CW.

For more from Jared Padalecki, pick up this week's issue of PEOPLE, on newsstands now.

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