The density of air at 20ºC (293ºK) is 1.204kg/m^3. At -10ºC (263ºK) its density is 1.341kg/m^3, or 11% denser. For a Model 3 moving at 100kph, about half of its power is used to overcome air drag and half is used to overcome rolling resistance. Air drag is 1/2 * density * velocity^2 * coefficient of drag * area, so an 11% increase in density means an 11% increase in drag, so a ≈5.5% decrease in range. That's significantly less than typical cold weather range loss.
Most of the range loss comes from climate control. In a combustion car, the majority of the energy in the gasoline is turned into heat. In cold weather, you just dump some of this heat into the cabin to keep it warm. An EV's efficiency is a disadvantage in this case, as it needs to use energy from the battery to heat up the cabin.
I don't have the exact numbers there but the HVAC system should draw ~2kW at full throttle. Giving an average of, let say, 160Wh/km (speaking of a recent Tesla M3 for example) at highway speed. Over an hour of full throttle heating you would have consumed in heating an extra ~10% of what you spent to move the car. So OK, maybe air drag increase is not the worst offender here but it's not just the HVAC system.
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While writing this I searched a bit and according to this [1] when there is really cold temperature and the battery still haven't got warm, it can draw 5-6kW at the beginning. Anyway when driving motors heat up, the heat is used to warm the battery, the battery heats up as well and all that heat is used by the heat pump to warm the inside of the vehicle.
I have a PHEV and when I turn on the heat as I'm pulling out of my garage, the range is cut by 30%. This has nothing to do with drag since I'm backing out at 2 MPH. It's just about the HVAC system, which uses a lot of power. I typically just use the seat warmer, but when my kids are in the backseat I have to run the heat as well.
I very much doubt this. I've never seen this having a notably measurable effect on ICE vehicles in Massachusetts winters (which can be cold but aren't notably arctic).
