The battery temperature, not the outside air temperature, is what matters. Your battery will be slightly warmer if it's in the trunk, considerably warmer if under the hood.It is charging at the moment, we'll see. 12.09V was after 3 hours of driving. Ambient temp around freezing if it matters.
It would help to know what car.
But 12.09V for a lead-acid battery is well below 50% charge, it's closer to 25%, perhaps lower. Even at 0C. That's a discharged battery. If the battery is warmer than 0C, then the state of charge is even worse.