No, I don't understand what the guy is asking, for serious. If he wanted to talk about the consequences of a tax on coal, then he wouldn't have stated his hypothetical as "absent coal."
If you tax coal and make it expensive, people won't use it. They'll use X, whatever that is. Hence his comment "absent coal". Now that they're using X, which is more expensive than untaxed coal, some people won't be able to afford heating their hut/yurt/cave/whatever and will die.
Coal wouldn't disappear overnight even if a tax made it uncompetitive with other sources of electricity. There's a ton of infrastructure that would keep it going for quite a while. That's why I can't reconcile "today, absent coal" with this idea.
Anyway, to your point, I think there must be better ways to help poor people afford energy than to subsidize the electricity of wealthy people and industries. Set aside a small portion of the tax revenues for helping poor people pay for electricity. The important thing with taxing an externality is to capture the cost, what you do with the money matters much less.
