The statue looks like the artist Frederic Remington's work. I have read some of his sculptures were in the White House.

"The Bronco Buster is the world’s most famous piece of American art. Frederic Remington presented it as a gift to President Theodore Roosevelt. The Coeur d'Alene Art Auction in 2012 sold at Auction one of the original bronzes stamped [Casting No.] 37 for $222,300.The Bronco Buster is the world’s most famous piece of American art. Frederic Remington presented it as a gift to President Theodore Roosevelt."

The link below has a picture of Ronald Reagan posing by it with another person.

https://worldofbronze.com/broncobuster-statue.html