Cold starting issue 99 Buick

Hi there, I have an odd issue with an older Buick. When it is cold outside like 30 degrees or lower, the car will not start or crank. As soon as I turn the key to start it goes dead like the battery is drained. When I wait a bit and it warms up to 40ish, the car fires right up like it was a new battery. When I say dead I mean all accessories and lights go out as if I didn't even have a battery in there.

The battery was recently replaced (1 month old) and never drained or needed a jump. As a matter of fact, I hooked up my Kia SUV to it to see if there was a current going from it and it never even turned on the dome light. I waited until it got warmer and the car started up without any external juice.

Any ideas? This is pretty squirrely and just started this winter. I verified the cables are tight to the battery and the cable ends are not corroded. They are snug to the alternator as well. I am really baffled and I don't use it often but I would prefer the car start when I need to use it :)