Remarkably, even most cloudy weather still lets a suprising amount of sun in. And it doesn't stop the wind from blowing. The threat is when the wind stops blowing at the same time it's very, very cloudy and in the middle of winter (short days). This happens, but it's very intermittent.

However, as seen above, there are lots and lots of ways to store (or equivalent) power over long periods, it's just the economic incentive to build them that is needed - and is now on the way. Renewable-gas low-duty-cycle gas peakers, Carnot batteries, and sodium-ion batteries are top candidates, with the first being the low-hanging fruit because they already exist.