This is a main drive battery, with a maximum output of 60 kW and a capacity of 12-14 kWh. It's designed to provide enough energy to drive the car. ICE cars may have trouble starting when it's cold because their batteries are weak. They're designed to only provide enough energy to turn the engine long enough to get it going. ICE car starter batteries typically have a capacity of about 0.5-1.0 kWh. In a PHEV, the main drive battery *may* have trouble providing enough energy to drive the car fast and far, but it's not going to have trouble just starting the engine, which is an extremely easy task for a battery of this size. And if the battery is having trouble driving the vehicle, the engine can take over (which is probably what you want anyway when it's extremely cold and you're actually using the waste heat from the ICE for cabin heat).
And when the battery is "empty", with 1 bar on the gauge (which is where the vehicle likes to keep it when it's running in hybrid mode), it actually has a 30% state of charge. If you have 0 bars on the gauge, that's actually a 25% state of charge, and there is a hard lower limit of around 19.3%, which the computer will not let you get below, even under sustained hard acceleration, like climbing hills, unless the vehicle is also low on gas. I believe the limit of emergency reserves (vehicle out of gas) is something like 13-15% state of charge so even then, it should have enough juice to start up the engine once you put gas in the tank.