Abelein was a passionate mountain climber. In 1977, while on a trip to help set up the Konrad Adenauer Foundation in South America, he climbed Mount Illimani (6,438m) in Bolivia. He also climbed the Hohe Munde (2,662m) in Austria in 1978. Between March and May 1980 he participated in the first European expedition to Tibet for many years, which climbed Mount Shishapangma (8,013m), the fourteenth highest mountain in the world.