In addition to reduced battery capacity due to chemical reactions slowing down in cold weather, if the car has a resistive heater, it will account for a substantial chunk of battery power. Unlike a combustion engine where the heater gets its energy from waste heat from the engine’s cooling system, electric motors generate little waste heat and all heating energy drains the battery.
Starting in 2020, Tesla, Kia, Nissan, and Volkswagen have replaced resistive heaters on some models with heat pumps (on some makes and models this is an extra-cost feature). Volkswagen claims their heat pump restores around 30% of the range that would be lost to the resistive heater in weather around freezing outside.
Here is an article about electric vehicle heat pumps from Current Automotive, “Model Y is the first Tesla with a heat pump. Here’s why that’s a big deal.”
Can the sensors compensate for snow, either snow on the things which must be observed - like road signs and road markings - or on the apertures of the sensors, themselves?
The sensors on Teslas are just cameras with, I believe, some near infrared capability as well as visual light sensitivity. The front-facing cameras are inside the windshield and take advantage of the wipers and washer. The side cameras are set high to avoid dirt thrown up from the road. The rear camera may require cleaning. All of the cameras have heaters to deal with snow and fog accumulation: this is like the heaters in LED-based traffic lights for the inverse problem.
Obscuration of road signs is precisely as much a problem for the self-driving cameras as it is for human drivers. Presumably the goal is for the software to be trained to do as well as a human driver with the information available.