This isn't a problem as long as your grid does dynamic minute by minute pricing.
When the price of power drops to zero in the spring/fall, you can be sure there will be plenty of people lapping it up to smelt aluminium, make glass, make steel, make cement, liquify air, make hydrogen, etc.
When the price of power is high in the winter, companies will swoop in with gas turbines, power cables from other places, and extra insulation to keep houses warm with lower energy costs. Entrepreneurs will see this coming, and will be there ready to provide power or power-saving measures to those who did not prepare.
As long as the market can set a price, the market will solve each problem. The people to lose out will be customers who don't adapt to keep their costs down - for example those who heat their 1960's uninsulated home with electric baseboard heaters.
There are already plenty of seasonal industries - like tourism. Power hungry industries will become seasonal or migratory too.