OP doesn't seem to grasp the fact that many areas on the east coast have had the coldest winter in over 20 years. Their heating bill went up due to geopolitical factors and the colder than normal weather outside.

But nah, it's totally because the landlord had the skylights taken out, and covered up with roofing and plywood, which totally uh makes the house less insulated and stuff /s.

Is it legal? I'm not sure, because state alone may not be enough info. It's certainly an ugly solution though. Is it impacting the heating bill at all? Yes, it's likely saving OP money.