Punishing politicians for bad weather seems like the height of illogic. But punishing politicians for responding poorly to bad weather makes perfect sense. The governor of Louisiana doesn't create hurricanes, but he can deal with a hurricane well or poorly. The upshot is that rational voters will punish politicians who respond worse than average to bad weather, and actually reward politicians who respond better than average to bad weather.
What does the data say? An excellent working paper by Andrew Healy once again finds that (1) voters do not measure up to simple benchmarks of rationality, and (2) less educated voters are especially irrational:
State-level presidential election returns show that a moderate drought has cost the incumbent party about 1.3 percent of the vote in farm states, with no significant effect in non-farm states. Individual-level voter survey data shows that a moderate drought has, on average, cost the incumbent party about 2.6 percent of the vote in rural areas in all states.
Voters with low levels of education are 2.66% more likely to switch away from the incumbent party after a moderate drought, a significant effect. In contrast, voters with high levels of education are only 1.41% more likely to switch and the effect is insignificant.
Healy's paper reminds me of a issue I've often puzzled over. Remember Yeltsin's single-digit approval ratings from the 90's? How much of that reflected his unusually poor handling of Russia's problems? And how much of it reflected the unusually severe problems that Russia faced? Frankly, despite all his mistakes, I doubt that anyone in Yeltsin's position could have been very popular. As far as the Russian people were concerned, the very best possible wouldn't have been good enough.