Plants store solar energy as hydrocarbons. Further reformed into coal, oil, and gas, that's what we use today.
It's possible to synthesize hydrocarbons from seawater at a net efficiency likely around 50%. Hydrogen electrolysis is the primary energy cost at 60% energy delivered on input.
Run that from solar cells at 20% efficiency and you've got a net delivery of 10% of input solar as stored hydrocarbons. Mind that you're only going to extract about 30-40% of that as useful work or energy (electric generation is about 38% efficient in fuel conversion, cars around 10-20%, IC engines generally about 30%).
But the neat thing about hydrocarbons is that once you've got them, they can store for a long time. Hell, we've got proofs-of-concept showing 300-500 million year viability.
There are other options as well. Some are far more responsive (flywheel kinetic storage, pumped hydro), some far more efficient in energy input/output), others have varying degrees of suitability (CAES, thermal energy storage, liquid metal/molten salt batteries). I'm actually starting to see this as a potentially solved problem.
More importantly, there is no reason the roads couldn't draw energy from the grid at times. Being subject to snow is very different from 24x7 snow all winter. If it is providing energy 80% of the time and drawing 20%, it may still be a net positive, especially when combined with enhanced safety and removing the winter maintenance budget line items (well, reducing, anyway).