The Matterhorn was an actual set location and actors and crew were required to climb the summit for filming.
James MacArthur made the film during his summer break from Harvard University where he was studying history.
Part of this movie was filmed in Zermatt, Switzerland. To the very day you can see where the Disney production company painted patterns on the outside of already existing chalets. These were added to be more in line with how Americans pictured an alpine town in the Swiss mountains. To the very day, when folks see the painted-on designs, many assume that they are originals from hundreds of years ago, however it was Disney who put them there in the late 1950's.
James MacArthur, Janet Munro and director Ken Annakin would all reteam the following year on Disney's Swiss Family Robinson (1960).
The Citadel mountain in the film doesn't actually exist, with the Matterhorn standing in for it. The real Matterhorn was only scaled for the first time in 1865, a year before this film is set.
Helen Hayes: James MacArthur's mother, appears uncredited as a tourist leaving the hotel where Rudi works.