HotRod wrote:
The engine doesn't move, I was wondering if maybe there was a relay or
something that could be effected by the cold? Where would I look?

Yes. No reasonable switch can handle the load imposed by a starter motor,
maybe 100 amps.

So, the starter switch really activates a starter solenoid which, in turn,
completes the circuit from the battery to the starter motor.

Follow the positive lead from the battery. It will go to one side of a
smallish cylinder (~2x4"). Another heavy cable goes from the other side of
this cylinder to the starter motor. It is this cylinder - called the starter
solenoid - that's probably at fault (they rust internally, stick, corrode,
or otherwise just quit). Replace it. Less than $10 at the auto parts store.