I've never seen nor had the cold affect the electrical system. I have to wonder if there was moisture that got frozen in the key switch.
The last two evenings when it was -10 to -15F temperature my Ranger would not start. It was like the battery was dead, although it was charged. Turn the key and there is nothing, although my interior light would work. No head lights, no power steering, no 4x4. I got an E code on the dash. When I would turn the key the fuel pump also would not cycle. We hooked up an external battery pack thinking it was a battery issue, but we had the same issue. Even hooked the battery pack up directly to the terminals and everything was still dead, minus my little LED interior light. Then randomly on try number 25ish of cycling the key to the ON position the fuel pump ran and it fired right up and worked fine. Once it warmed up I turned it off and it fired up multiple times both evenings. This morning it was -2 and it started fine. I brought it to the dealer and they found no codes. We replaced the ignition as that is the first place they thought to start. I am thinking it may be a wire harness issue and the wires are somewhere are not making contact in the cold and therefore not letting the engine cycle. Very frustrating. Anyone have any similar experiences? It seems to be a crap shoot at trying to diagnose the issue. HELP!!