As for “at night”, it is possible to get batteries of household scale. Plus insulation is getting better and cheaper, so the power required to maintain any given temperature isn’t as high as it used to be.
At times of the year when there are blizzards, I seriously doubt the rest of solar installations in the US are going to be running anywhere near capacity.
Second: My first visit to the USA, I saw people surfing in Asilomar on Christmas Day/Boxing Day and it remained warm and sunny throughout my stay in California, yet a few days into that trip New York was suffering a blizzard that Trump was trying to argue disproved global warming: https://en.wikipedia.org/wiki/Early_2014_North_American_cold...
You're assuming they have an infinite lifespan. They don't.