My engine will not start up and run?

There are a number of things we need to start with. First and foremost is scanning for codes.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Next we need to have the battery load tested because you may be correct that this is a battery issue.

https://www.2carpros.com/articles/car-battery-load-test

If these do not pan out then here is a guide on this issue in general. We need to start working through this.

https://youtu.be/dCjmRL3p4Cs

Let me know what questions you have questions but if these things are not the issue I am putting my money on a fuel pump issue. However, the cold weather points to a battery. If working through that last guide you get to a fuel issue here is a final guide on how to test the fuel pressure:

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

Let us know what you find. Thanks