The OP article suggested that many people ordinarily use propane heat, which normally can be delivered just fine. I don't know enough to say why not firewood, but I'd guess expense and convenience. Aha, this other article mentions a firewood shortage, but doesn't say details:
> In homes heated by firewood, there is another battle. Yellow Hair says there is a firewood shortage happening on the reservation, but communities are coming together to help one another. “Lending that helping hand, when they can and where they can,” said Yellow Hair. Keeping people warm is an issue across much of the Pine Ridge Reservation, with a firewood shortage and propane trucks jelling up from the cold.
—https://www.blackhillsfox.com/2022/12/22/one-natural-phenome...
And here's an article about life in Pine Ridge generally:
> Among the most impoverished of these reservations, Pine Ridge is plagued by an 80 to 90 percent unemployment rate with a median individual income of $4,000 a year, according to the Re-Member nonprofit organisation’s 2007 statistics.
— https://www.aljazeera.com/features/2016/11/2/life-on-the-pin...