He competed for Poland in the 5000 metres at the 1960 Summer Olympics held in Rome, Italy, where he won the bronze medal.

He finished just a fraction of a second behind the German runner Hans Grodotzki, who was in fact born only a few miles away (in Pasłęk) from Zimny's hometown in Tczew, in northern Poland.

As of 2024, Zimny remains the only Pole, male or female, to have won an Olympic medal in the 5000 meters.

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