Whether the weather increases volatility of markets

I recently read, and thoroughly enjoyed, the book Rigged. In one scene a young trader is asked what factor contributes most to changes in the price of oil - to which he responds, the weather. For example, a cold winter in North America or Europe signals an increased demand for oil and sends the price up. 

So my question is this. Given how weather dependent our agricultural industry, our energy industry, and other essential primaries industries can be, how much less volatile would financial markets be if we had predictable or constant weather?

Funnily enough, there are plenty of people out there studying this exact question. Really. You can find papers seeking to find weather effects on various stock exchanges around the world here, here, here, here, here and here.

Much of the research finds that cloudy days and sunny days do not impact the functions of the market. As a general rule, the more efficient markets, with traders from various locations, are more robust to the weather effect.

But the question here is not about whether the weather has psychological affects on trader behaviour (which is the focus of much research), but whether extreme weather has real impacts on the demand and supply of various commodities. One can imagine that an extremely cold winter in Australia would increase demand for energy, while at the same time decreasing the supply of winter crops, such as wheat, that are affected by frost. There must be an obvious link, but maybe not an obvious outcome.

No doubt there is a link between weather and the economy, and maybe that goes some way to explaining why the simplifications of economic theory provide such poor forecasts. If economists can stay ahead of meteorologists in their forecasting ability, maybe they are actually doing alright.