A Colonel in the Argentine army, Enrique Padilla played at number three for Argentina at the 1924 Olympics, and took part in all four of their games, moving to back in the final game against France as the team was re-shuffled to bring in Guillermo Naylor. Padilla went on to win the Argentine Open on two occasions, both times with Hurlingham. Playing for the Hurlingham “Martin Iron” team in 1926 he, along with Francisco Ceballos, Ramón Videla Dorna and Justo Galarreta, made history as the first all-native Argentines to win the Open. Padilla won his second Open title with Hurlingham “Blues” in 1929.
A 7-goal handicap player Padilla also served as a vice-president of the Argentine Polo Association. His other victories included the Anchorena, Filiberto de Oliveira Cézar, Ladies Nomination, and Ravenscroft Cups.
Argentina