Oxholm first appeared internationally when he won the bronze medal in the all- around at the 1978 Junior World Championships. Before that, he had already won several national sprint and all-around championship titles. The year 1980 was Oxholm's most successful. In addition to winning two bronze medals in all-around competitions at the European and World Championships , he was able to qualify for the Winter Olympic Games in Lake Placid . There he was third in both the 5000 meters and the 10,000 meters. In the following years Oxholm reached the podium several times at national championships and placed in the top ten at international competitions and championships . However, he was no longer able to build on the successes of 1980.
After the end of his active career, Oxholm worked as a trainer, including for the Norwegian sprinter team and as the private trainer of the future Olympic champion Ådne Søndrål .