The increased aerodynamic drag of a strong headwind will have a dramatic effect upon battery consumption, and the following graph shows how a small increase in speed will greatly increase the required power to maintain that speed:
According to the above graph, a typical motor would draw ~110W @ 15 mph
(on the level with no headwind). If you were travelling at 15 mph with a constant 10 mph headwind, the wind resistance
(and the required power to overcome it) would be very similar to travelling at a constant 25 mph with no headwind.
This would produce a much higher current draw of ~500W and would also reduce your battery's range to ~22% of what it could manage at 15 mph without any headwind.
If you typically had a 20 mile battery range at a constant 15mph, this range would be reduced to just 4.4 miles when riding into a constant 10 mph headwind.
If you then add extreme cold temperatures and steep hills into the equation, the poor battery will be subjected to a really hard workout.
Low ambient temperatures may be good for magnets, wires and motors, but lithium batteries tend to be more like me, and I really don't appreciate low temperatures.
Alan