Re: electric heating
Even if you ignore snow, mounting solar panels flat is probably suboptimal anywhere in the US because of sun angle, and
https://googleblog.blogspot.com/2009/07/should-you-spring-clean-your-solar.html describes how Google found that manually cleaning flat solar panels was worthwhile for maintaining their output, whereas even a 10 degree angle away from flat seems to be enough in typical conditions for rain to rinse off the solar panels adequately to make the results of manual cleaning pretty much unobservable.
While electric resistance heating is indeed generally inefficient, ventilation issues can sometimes be somewhat a mitigating factor, and heat pumps also exist which are more efficient than resistance heating.
IIRC, the new Footprint Power station in Salem, MA is a combined cycle natural gas plant that is going to have 58% efficiency. If you could combine that with a heat pump with a Coefficient of Power (COP) of 2, that ought to mean 116% efficiency compared to burning the same natural gas directly (if we ignore transmission / distribution losses on the electric grid, and ignore the heat wasted from providing ventilation to whatever is burning the natural gas in the home). But on the coldest days, we're likely to have some less efficient natural gas (and oil) plants running for the next several years; it may be that burning natural gas directly in one's home on the coldest days and running an electric heat pump for heating on more mild days (when the warmer temperatures will improve COP and the grid will be running cleaner) would end up minimizing fossil fuel consumption.
And in the long run, it would be great if we had so much electric power in the winters from wind that we could convert to heating buildings with wind power, but I suspect if we make any real progress in that area we'll have a huge oversupply of power in all of the non-winter seasons, which would make the economics of building those wind turbines a lot more challenging.
In the context of a stove top, if you have a building insulated to some approximation of Passive House standards, the typical practice would be to use an Energy Recovery Ventilator (ERV) for bringing fresh air into the building as a whole. Some sources say you can use a range hood that recirculates air to collect the cooking grease in its filter, and then from some point in the kitchen away from the stove top, pull air into the ERV to be exhausted to the outdoors; other sources suggest that if you have natural gas or propane burners, the ERV won't necessarily provide enough airflow to maintain good air quality in the kitchen. If it turns out that a natural gas burner means you need a bunch of airflow that can't pass through the ERV, and you wouldn't need that airflow with an electric burner, and you heat the makeup air coming into the building to 50F or 60F in the winter, it wouldn't surprise me if the electric burner would end up using less total energy when you include the energy wasted heating the make up air. But as far as I can tell, the science regarding how much airflow you need for a stove top in a tightly insulated home has not been investigated as far as it should be.
The Tesla Solar Shingle product is the roof surface itself, not a separate solar panel thing. If you just melt a thin bit of the snow that is directly touching the roof, much as that seems like the obvious right way to solve the problem with minimal energy consumption, I'm not sure how you get a reasonable result once the snow reaches the rain gutter.
(I'm also not entirely certain that Tesla's snow melting solution has the efficiency of a resistance heater and not a heat pump, but I have seen nothing that would lead me to believe it is going to deliver heat pump level efficiency.)
