How do the north repopulate after harsh winters?

The usual way, I suppose. 

But seriously, the sad reality is that, while you always have to be worried about population declines leading to production declines and a vicious spiral, the upside of a drop in population in an economy like the North is that the GDP per capita increases greatly. 

The barns, farmhouses, fences, granaries, and land don’t go away during the winter, so they’re there to be claimed by whoever survives. With more wealth to their name, people get married earlier, have more kids, and have better levels of nutrition and health, which means more kids surviving infancy and more people living longer. 

So most likely, the North goes through something of a population boom in the springs and summers.