I just got through watching this again and I just noticed something, when they go out to get Rodregez from under the wrecked jeep you can see the snow melting on their helmets. So some of it was filmed on location somewhere other than in Culver City and in a studio sound stage.
shareThe movie was filmed in several locations one being Fort Lewis Washington. Those scenes, from what I understand, are the opening camp marching scenes, the end sequence, and several "cold" sequences while the rest were sound stage.
They also used some archive footage from WW2 as far as I know.
IMO the snow used in the scene where Ricardo Montalbán ("Roderigues" or Rodríguez) hides from german troops is fake.
I recall seeing part of an interview with Van Johnson, I believe on Turner Classic Movies, where Johnson mentioned the artificial Pyrene "snow" used in some of the scenes.
As I remember correctly, Johnson said the scenes were filmed on a huge indoor sound stage at MGM, and the technicians had snow machines going up in the rafters which created enough "real" snow to fall -- and realistically melt on their helmets -- in closeups.
I think he also remarked the actors were constantly getting their eyes stung by the artificial Pyrene "snowflakes" that were being dropped on them in other scenes.