Miloslav grew up playing in Kladno. He played for PZ Kladno between 1969-77 and then continued to play for Poldi Kladno in the Czech league as an adult. Miloslav wasn't the easiest player to coach when he was a youngster. He didn't like to listen to the advice given to him by older players and coaches. He was very outspoken and often said things that didn't sit well with people around him, mostly coaches. His coaches let him get away with a lot of stuff because he was a great talent, and he displayed that talent best when he got some slack. In his early years he was an offensive defenseman with a booming shot. He had one of the better shots in the entire Czech league.
Miloslav's long time dream of playing in the NHL became a reality when he laced 'em up for the NY Rangers at the end of the 1988-89 season. He played six games. Before the 1989-90 season was to begin a lot of changes happened in New York. Miloslav had to start from scratch during the training camp. He played so well that he earned himself a regular spot on the blueline for the 1989-90 season
Miloslav was greatful to his Swedish teammate Tomas Sandstrom who helped him a lot. They used to play against each other in Europe. Sandstrom gave him valuable advice.
"Now you are in America, which means that everything for you will be a new experience. Try to adapt to the flow of the game, because if you don't then you'll be history pretty fast," Sandstrom advised "There will be times when you'll hit rock bottom. You'll come up with thousands of reasons to leave and go back home. Don't do it, there will be times when you are dead tired, but you have to dig in and continue. Around you there are a lot of wolves who can't wait until they can get a bite of you, get rid of the uncomfortable European. There will be moments when you will be ready to throw in the towel, but you have to fight through it and work even harder.Just smile and stare them in the eye, and tell them them that you expected it to be a lot worse. That way you'll earn respect and the guys who want to take your spot will be perplexed, asking themselves: ' we are down on our knees and this Horava guy is still going.' This will eventually cut you some slack."
Sandstrom's pep talk was really important to Miloslav who often thought about Sandstrom's words when he had doubts about himself. The change wasn't just huge on the ice but off the ice as well. Miloslav barely could speak English and he wasn't used to all the luxury given to him by the Rangers. They fixed him a huge house in Rochester and a fancy car. Miloslav, who was a pretty well travelled fellow, was impressed by how professionally things worked in the NHL.
He also admitted that he didn't realize how stereotypical an NHL'ers life was. Eat, sleep, travel, train and play hockey day in and day out. The rebel in Miloslav was still present and he had a hard time to cope with the constant roster changes. One day you were in and the other you were out of the lineup without any explanation from the coach.
After the 1990-91 season Miloslav left North America to play in Sweden and Modo. He was one of the best defensemen in the league and played there until 1994. He then went on to play for Slavia Prague in the Czech league and Karlovy Vary, also of the Czech league. He retired in 2000.