Wind works well in the winter, so the the renewable heating tech I would expect to be economic is: wind, cold-tolerant battery technology,& heat pumps. The first is well solved (worked for TX). The latter two are too expensive for now, but no reason to think we won’t travel down the learning curve.
Fair. What about long-term heat storages? Nordic countries in Europe seem to count on that (at least in part, see Finland).
I recall hearing about molten salt systems, but just burying your ground sourced heat pump a little deeper is a semi efficient way to store heat. Requires a lot of space though. Synthesizing e gas would be a compelling technology if it develops. Then you turn summer sun into fuel for winter.
I believe a big obstacle to e gasoline is political economy. Deploying this means buildings would have oil furnaces. These could of course be fueled by fossil fuels, supporting demand for those fuels.