Neither of the fans is going to operate in this cold weather, the engine fan is controlled by a thermostat and only comes on when the engine is really hot (probably above 95 deg C). The other fan is controlled by the aircon, and when aircon is operating both fans come on anyway (one for engine cooling and one for aircon refrigerant cooling). The fact that you have had the heating on full blast makes it even less likely that the fans will come on because you are dissipating engine heat via the heater radiator into the car.
The heater gets priority for any hot water that is available before any gets passed to the big radiator. This is controlled by a mechanical (wax pellet) thermostat that opens and closes a valve in the cooling system, when the engine is below about 80 to 90degC the thermostat stays closed and water is only allowed to heater, when thermostat opens water can go to to both heater and big radiator. Modern engines have a lot less liquid in the cooling system than they did say 10 to 20 years ago, this allows the engine to warm up more quickly and saves fuel.
I don't see the point of leaving the heating off in this cold weather, otherwise how do you defrost your windscreen, the car and your feet. Just leave heater control on screen only or screen and feet and that restricts the amount of air going through the heater anyway to minimum needed.
Just another thought, where does the heater in a battery car gets its energy from - from the batteries? Surely that will take a lot of power-------? I know air cooled VW engines used to have a heat exchanger around the exhaust pipe to get heat into the car.
