Horwitz was born in Santiago, Chile, and is Jewish. His sister Nadja Horwitz represented Chile in sailing at the 2016 Summer Olympics in Rio de Janeiro, in the women's 470 class. His cousins Henrik von Appen and Sven von Appen represented Chile in alpine skiing at the 2017 World Championships in St. Moritz, Switzerland, and Henrik competed for Chile at the 2014 Winter Olympics and 2018 Winter Olympics in all five alpine skiing events. In 2018, Henrik was also Chile's flagbearer at the opening ceremony.