Some of these numbers are a bit off, but generally the point is correct.
An average Central air-conditioning unit (compressor and fan) uses about 3500 watts, so 3.5 kWh
BTU’s are an energy unit, and equate to 0.293 watt-hours. 100k btu is on the high end of a normal home furnace, but ok, so that equals 29.3k watt hours.
So, yeah, heating takes a lot more power, generally.
More importantly though, to address the feasibility of running this off solar… At ground level, the total energy density of sunlight is around 1kW\m².
So if you had magical solar panels that somehow converted solar into usable energy with 100% efficiency, you would need about 30m² of solar panels to produce enough power to translate into the heat put out by the average furnace.
But solar panels aren’t that efficient. They are only at around 20% now. So to put out the power equivalent to the average home furnace, you are talking 150m² of solar panels, per home. And that’s only if they are producing that much power in ideal solar collecting conditions.
Technically, the average home has about 140m² of roof, but you can’t use all that space, because of course you need to angle them towards the sun. So you generally only have half of that space, at most.
Even if you assume some kind of efficient battery tech that can store the power during the day, maybe you can assume that since a furnace doesn’t run all the time, it might be a wash with the fact that you are only gonna get sun during the day… But still, the average home isn’t going to be able to produce enough power to heat itself in colder climates, just due to limits in the space available for solar panels. You would need dramatically more efficient solar technology than what we have now.