1995 Monte Carlo wont start when cold out

So this winter has been driving up the wall with this problem. I am a student and I get up and go out to start my car in the mornings. Nothing. I hear a click. With my past experience with cars I figure ok battery is dead. Replaced battery still happenes. So I then replace the Solenoid. Still happens.

This only happens when it is cold outside, like 38 or below. When it gets up for 50 she starts up fine. Also when I do get it started the rest of the day it starts fine. There have been a few times though that I turn it off and then try to start it like 10 mins later and it doesn't start. I have to sit there and keep trying it until it finally starts. All help is appreciated.