Cold Weather Car Starts

When the temperatures drop to the single digits and below, my car won’t start. It won’t even turn over! I turn the key and there’s nothing. So, I sit in the car and then turn the key again. I wait. Then turn the key again. Within about 5-10 minutes, the car starts and its good to go! I’ve had a new battery installed. And even with the new battery, it does the same thing. At the shop, they check the battery and say it’s fine. Can anybody help me?

Next time it acts up turn on an interior light and crank it.
If the light stays bright it’s the ignition switch, starter solenoid or wiring to the starter.
If it goes dark it’s a wiring problem elsewhere, like a corroded connection.

Thank you. I’ll give this a try.