Miloslav Hořava started his career with TJ Poldi SONP Kladno in the Czech league in 1978. He stayed with them until 1983 when he moved to HC Dukla Jihlava, returning to Kladno in 1985. During this time he competed for Czechoslovakia multiple times, starting at the 1979 European Junior Championships, and later playing at the World Juniors in 1980 and 1981. He played at the 1982 World Championships and Canada Cup, before representing Czechoslovakia at the 1984, 1988, and 1992 Winter Olympics, and competing for the Czech Republic at the 1994 Lillehammer Olympics, winning two Olympic medals, a silver in 1984 and a bronze in 1992. He later played at the Worlds in 1985, 1987, and 1993. Hořava had a short stint in the National Hockey League (NHL), playing three years with the New York Rangers (1989-91), but played a total of only 80 games in the NHL during that time. After his NHL career he played three years with MoDo Hockey Örnsköldvik in Sweden, before returning to the Czech Republic in 1994, playing six more years with HC Karlovy Vara, ZTC Zvolen, and HC Litvínov.
In 2002 Hořava began a coaching career in the Czech Extraliga, working with HC Znojemští Orli, HC ČSOB Pojišťovna Pardubice, HC Karlovy Vary and BK Mladá Boleslav. In 2009 he returned to MoDo Hockey Örnsköldvik, to serve as their head coach.