No crank when cold out

I've had this happen twice now. I'm leaning towards the solenoid on the firewall. When it sits for a cpl days in extreme cold, I turn the key and nothing happens. No click, nothing. This morning when it happened I tapped in the solenoid and in the second turn of they key she spun over strong and fired right up. Any ideas??

 

The reason I asked the question was to verify what I thought. But thanks for your input

 

Thanks. All contacts were cleaned and tightened recently when I replaced the starter. The only thing I skipped over was the solenoid. I didn't think it would be susceptible to extreme cold

 

I'm not sure if there is such a thing as cold weather version. It's not an expensive part so I'll change it and see what happens. Might even wrap it with some sort of insulation, not sure if it would be beneficial though