Yes, moderate supplementation seems like a good idea, especially at higher latitudes. I'm not sure how likely toxicity through overdosing is, but ultra-high dose vitamins aren't a great idea in general.
In the UK, the NHS
has been offering free supplementation for Covid high-risk groups. There's also a recent report by the BMJ
here.
From what I've read, it seems like only people with serious Vitamin D deficiency ought to take the supplements. According to
this article from PubMed hospitalized patients with a severe vitamin D deficiency had a much higher mortality probability against the ones that didn't (50% against 5%).
However, everything is not that simple with coronavirus and
I strongly encourage people without the deficiency not to take any supplements. Not only due to toxicity, like you pointed out, but because of the virus's peculiar features.
It has been found that Vitamin D increases the expression of the ACE2 receptor, which is a binding site for the coronavirus. In other words - there will be more contact points between the cells and the virus, thus, there's a risk of increasing the number of infected cells by making it easier for the virus to penetrate.
People should really be careful with self-treatment, even if it's something as innocent as the vitamins, and consult with professionals.