How about this:
When you're out in a snowstorm (i.e. only roll once between encounters), roll+hard. On a 10+, you're fucking freezing but of you keep moving, you can probably make it. On a 7-9, you're wearing down, add 1 to your frostbite clock. On a miss, the cold is too much for you: Add 1 to your frostbite clock and take 1-harm for each segment on the frostbite clock.
When you get back inside and warmed up sufficiently, erase all the ticks on your frostbite clock. If you go back outside right away, though, touch luck.
If you're totally unprepared to be out in a snowstorm, wearing all the wrong clothes and shit, take -2 to your roll, as if you're being interfered with. 'Cause you are, dumbass.
The MC may add a tick to your frostbite clock, or make you suffer harm equal to your frostbite clock as the result of missing other moves performed in a snowstorm, as appropriate to the situation.