Horvat is regarded as one of the "central figures of the new left in post-Yugoslavia". He has participated in different activist movements across the world, including the 2009 student protests in Croatia, Occupy Wall Street in 2011 and World Social Forum in Senegal and Tunisia. He has visited the 2017 G20 Hamburg summit which he described as a "dystopian nightmare", claiming that "the real problem is the dogmatic slumber of the leaders of the free world, represented at this G20 summit by Merkel, May and others, which is the origin of our current dystopian nightmare (wars, terrorism, the refugee crisis and climate change)". Since 2016, he has claimed that "the need for a progressive international movement was never as urgent as today". Asked about what the Facebook–Cambridge Analytica data scandal meant for the future of politics, he claims that "in the near future this will be remembered as the early days of a much more radical transformation of what we understand under politics". In 2017, Horvat signed the Declaration on the Common Language of the Croats, Serbs, Bosniaks and Montenegrins.