He obtained a doctorate in theology on 25 November 1869 from the Royal University of Budapest, where he also taught biblical studies from 1862 to 1869.

Hornig served as private secretary to Cardinal János Simor of Esztergom during the First Vatican Council (1869-1870), and then as Rector of the Budapest seminary from 1870 to 1878.

Following his creation as Privy Chamberlain of His Holiness ad honorem, Hornig was named titular abbot of the monastery of the Blessed Virgin Mary of Babolcha.

He received his episcopal consecration on the following 8 September from Cardinal Simor, with Bishops Janos Zalka and Kornel Hidasy serving as co-consecrators.

Hornig was one of the cardinal electors who participated in the 1914 papal conclave, which selected Pope Benedict XV.