ah

someone else who knows what cold really is

. i'm an alaskan...
in the -30 range, some components will simply contract to the degree that factory "room temperature" tolerances are exceeded, and things stick. i have this problem with my temperature knob when the temp drops below about 10*F.
it could be a contact, it could be a tolerance problem, honest cold (not that 30*F nonsense that people whine about here in ohio) is generally not something designed for--much below the temps you're experiencing, most cars dont even start due to frozen fluids and lost tolerances--i'm sure you're no stranger to outlets in the grocery store parking lot for block heaters

.
some ideas: check the tolerances when it's bitter cold--might have to take it apart and leave it outside, then measure...-30 is no laughing matter, no time to be working outside on a truck. also check the continuity through the fan.
i'm guessing it's caused by contraction of dissimilar materials, but it could be hell to track down.
a couple things i do in winter when i know it'll be cold enough to freeze knobs and dials is leave them where i'll want them in the morning, but in the case of moving parts like a/c compressors and fans, i leave them off until the truck has warmed up. i don't know how they'll react to serious cold, i've driven through it (-20*F) in a tundra but not had to start the truck in the morning in those conditions.
good luck,
-sean