Will not stay running

Your car has 2 fuel filters. One is inside the tank mounted on the fuel pump while the other is mounted on the right side frame rail. The one on the frame rail is usually the one that fails first. Replacement involves draining off the fuel pressure by removing the fuel pump fuse, then you start the engine and let it shut off, then try starting it again. The pressure should be out of the system. Then Then you need to raise the vehicle to access the filter. It has one clamped line and one quick disconnect line that you will need the release tool for. Then you remove the bolt and filter and install the new one.

However you may want to test the system first as those symptoms could also be caused by other things. When you start it, how long does it run before stalling? Any check engine or security lights? Did this just start when the cold weather hit (if you're in the cold areas)?

Okay, that could be filter related or you may have contaminated fuel. Will it reliably start and shut off every time or does it start and die and then will not restart? If the first one is the common one it likely isn't the filter itself. Normally if it's a bad or contaminated filter it will reduce engine power but not let it run and then quit. That sounds more like the fuel pump isn't staying powered and for that a fuel pressure test would be the first step. See if there is pressure on the initial start which then drops off.

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

Another item for the filter, how was the engine running prior to the cold weather? Good power and no issues? If yes it's likely not the filter unless something odd happened like someone dumping water in the tank.