Perhaps. But then that means the power lines need to be maintained, even when not in use. I'm not sure what the amount is, but it's probably not insignificant.
We would need a gigantic store for heating our house, because for 4-5 months a year, we are generating less electricity than we need. Something on the order of 15MW of storage.
We could certainly our home's thermal efficiency, though this would be complex. We could also add more panels, but then we'd be overproducing by even more during the summer.
For context, I live in the cloudy-ish south of Australia, and have similar problems with our solar power in winter. However, we still produce reasonable amounts of power through the day, and our total winter shortfall is only about 500 kwh, once offset against the daily production.
So for us, 500kwh -> 2080.8 MJ -> 462.4 litres of storage required (assuming 4.5 MJ / litre and ignoring round trip losses), which seems an entirely reasonable for local storage, safety aspects not withstanding.