The White Tower (1950)
The White Tower is a 1950 mountain film starring Alida Valli as a woman determined to fulfil her father's dream by conquering the mountain that killed her father, and Glenn Ford as the mountaineer who loves her. It is based on the novel of the same name by James Ramsey Ullman. She assembles an unusual climbing party of six people in the Swiss Alps to tackle the nearly impossible ascent of a mountain known as 'The White Tower,' which has never been climbed. While struggling together to conquer the obstacle, each climber shows his true worth, or lack of.
More at Wikipedia.