The household never seemed particularly poor in my eyes, though. So, they should have made the same kind of preparations for the next winter well beforehand.
It's not, but they also don't hire on labourers, they do it themselves. So it's just whatever they have available, basically. It also looks like they get pretty mild winters in general, so probably can get by by doing that. This said, Nyako taking so long to get more firewood when it was already running out such that it goes out and the entire house gets cold is a problem; she should have been able to collect a fairly large bundle of sticks to keep it going long enough to get even more before it died, enough for several days, and they should have had larger pieces of wood drying under a shed from the year prior, too, to be processed into lumber or firewood as needs be.