A Swiss branch of women's group Zonta Club and the Europa Donna Suisse association organised the challenge to illustrate "the fact that women suffering from breast cancer can go beyond her own limits."
The women will sign a declaration on their return from the 13,120-foot Breithorn summit in Switzerland to call on politicians to allow better access to breast cancer treatment, which they say affects one in 10 women in Europe.
One of the event's organisers, Bettina Borish, a Geneva-based doctor, said 15 new cases of breast cancer are diagnosed in Switzerland each day.
She told the Swiss daily Le Matin that differing standards in treatment across the country's regions (cantons) and a bureaucratic federal health system hampered women's access to the right care.
Borish says there are on average 5,267 new cases of cancer in Switzerland each year. Breast cancer has become the main cause of death for women between 45 and 65 years old with 1,355 deaths a year.