Managing the stock of firewoods in Banished is a crucial tactical point. It is enough that this one is close to zero during the winter periods, so that the population becomes entirely decimated by the cold in less than few minutes.
It is therefore necessary to maintain and increase this stock all the time. Manage forests, as well as wood cutters.
To do this, install logging lodges in several places around your city. For the first few years, just plant and not cut the trees. Next, harvest the wood from the forests that are not yet maintained. Near each lodge, build a storage pile for the logs, and a woodcutter.
When you need more firewoods, then you just have to disable the planting and activate the cutting.