Some additional thoughts:
In practice, even if the heater is running off main-AC, one would not walk out to a snow-free car, hop in, and go. In practice, brushing off snow is going to be necessary whenever snow is reasonably heavy.
Think about it, if you have say 1/2 meter of snow on your car. Running of main-AC, you can melt all the snow on top (roof), but the heat will have problem reaching your front-hood. So, the windshield may be clear but you will be looking at a mountain of snow on the hood preventing you from seeing the road. So brushing off snow is to be expected regardless of how much energy you got in your batteries. Once you have to brush off snow on the hood, brushing off snow on the car roof is not that much more added difficulty.
If I am the user (in the Mid-West USA weather), my concern would be ice. Snow can be brushed off easily. Ice stuck to the windshield is a pain in the behind to remove. So you just need enough heat to ensure that the windshield and other glass-areas are ice free. You would have an easy job of merely brushing off loose snow.
But not so fast -- don't forget, as snow melts, the melt will turn into ice almost immediately -- think about the icicles around the roof on your house. Your house probably stay heated all day, but icicles still stick around all day.
Therefore, one concern I have would be melted-snow refreezes, and icicle formation. Trying to open the car door with a 5mm (or 1/4 inch) of ice shell covering it is a pain. Now you have a problem a lot worst than what you started with which was mere snow, and that ice covering the lower part of your door probably was the snow that was on the car roof.
Since every car design is different, it would be hard to estimate how much heat is required to ensure all the glass around it being ice free, and the doors are not ice-covered. There are so many variables (wind, ambient temperature, amount of snow cover...) over-sizing the capacity will likely be a necessity. And, you need some mean of maintaining that heat till you get into the car -- you don't want to get back to a big icicle.