Depending on how much time or emphasis you want to spend on their trek, you could run it as a single roll (a consequential contest), with failure resulting in an exposure-related consequence. A series of "attacks" works well, as others have said. Except I'd argue that you don't need to worry about killing the PCs; you decide what happens if you take someone out, so they only die of cold if you say they do. The PCs could "attack" a stress track representing the distance to their objective with Endurance or Athletics or Survival, or set up Blocks with Survival as they create makeshift shelter or Declare emergency gear, and so on.
If I were to run this as a scene where I wanted to endanger the PCs but didn't want to spend time on it nor really, really threaten them, I'd run a 2-step content. The first roll would be the storm's attack against Survival rolls; I'd inflict stress/consequences here as normal, and to me this would represent taking proper precautions, knowing which way you're going, staying out of the worst of the storm, wearing the right gear, and so on. PCs who failed the Survival check would then be subject to a second attack against Endurance. Difficulties would vary according to how bad the weather would be, I suppose. I'd probably set them at 3 or 4; anything less and I don't think I'd bother making it a contest at all; just place a scene aspect and keep moving.
