Car makes ticking noise when trying to start

This sounds like a battery that is not robust enough to handle a starter motor drawing enough amperage to turn cold engine with thick oil in it. I would test your battery first and then charge or replace it from there. A frozen fuel line would allow the engine to crank as normal but the engine would not start, due to the lack of fuel delivery. At -3 degrees, it is not shocking or abnormal to expose a weak battery.