Baena was born in Altamira, Caracas. He completed his primary and high school studies at the Colegio Simón Bolívar in Caracas. He speaks German, English, Spanish and Swedish.
Cesar is the only and first Venezuelan athlete in Biathlon Sport. In 2007 he trained for the South American Biathlon Championship in Chile. In 2008 in Bariloche Argentina. On 2010 he did in New Zealand.
While living in Germany he started to ski at age of 19.
In 2008 he trained in Austria. He was the first Venezuelan Skier at Kangaroo Hoppet 18th edition in Australia, racing 42 km. As well the first of his nation to compete at the Australian National Championships. At the year 2009 he competed at the Merino Race in New Zealand and won the 7 km competition. In 2012 he represented Venezuela at the Vasaloppet; one of the largest cross country ski races in the world.
In 2009 he took part in Nordic Skiing World Championships in Liberec placing close to last in each event.
Late 2009, he became the first South-American Cross Country Skier to participate in World Cup representing Venezuela, and twice, in Düsseldorf Germany 5 December 2009 and Davos Switzerland 12 December 2009. As well on January 2013 he competed at the Sochi World Cup Sprint event in Rusia.
Along with his brother Bernardo Baena he participated at the Oslo 2011 World Ski Championships, racing the 10 km classic qualification, the free sprint, the pursuit, the team sprint, and the 50 km mass start race. Bernardo and Cesar, as Venezuelan team, were the only and first Latin American team to compete in the sprint relay in the Nordic Ski Championships history. Also competed in the 10 km individual qualification.
Cesar Baena set on July 5, 2012 the Guinness World Record for the longest roller ski trip. The journey took 57 days and started in Stockholm; following the route to Mora, Sälen, Hudiskvall, Östersund; where he crashed with a trailer hurting his leg and after covering 2,246.21 km ended up in Holmenkollen on the independence day of Venezuela (5 July) on 2012.