Overheating light

Just because it is cold out does not mean your engine is not overheating. Check the coolant level.

I checked the coolant and also the engine wasn't overheated. I mentioned the air temperature because this is my first winter in a jeep and I didn't know if the cold temperatures outside would trip a sensor

If you are certain the engine is not actually overheating then the coolant temperature sensor may be bad.

How did you solve this problem? I am facing the same problem and unable to start the car.