In February 2024, a number of graphic videos (which were shared from his own Instagram account) were leaked online showing Parra abusing horses with whips, ropes and other devices.

[2][6] The Oldenburg and Hanoverian Verband banned Stefan Sandbrink and Dr Kerstin Klieber, two individuals pictured in the Parra videos, from participating in the associations activities until 2028.

[8] In 2012, he appeared in court to answer to two criminal complaints alleging "torture" and "torment" of a living animal, after a horse being trained by Parra fell while being lunged, causing lasting injury.

[11] In 2021, Cesar Parra and Belle Ami were announced as the winners of the 3-star Intermediate I and I-1 Freestyle at the Dressage at Devon horse show.

Riding for Colombia, he participated in the 2004 Olympic Games, in Athens and the 2005 FEI World Cup Finals, in Las Vegas.

[16] Since gaining his US citizenship in 2008,[17] Parra was part of the Team Gold Medal at the 2011 Pan American Games in Guadalajara, Mexico.