1995 Pontiac Grand Prix Car won't start

The vehicle ran just fine the day before. The weather got extremely cold overnight and now it won't start.

When I turn the key the lights automatically come on (normal) when I turn it further, the lights just blink, no clicking noise, nothing.

I replaced the battery. Same exact thing

I did a volt meter test on the starter and received a reading of 12.46

It is still very cold and still won't start.