How does bad weather influence elections?

It does, and there is a new theory of how, from Erik P. Duhaime and Taylor A. Moulton.  Here is the abstract:

While political experts have long claimed that bad weather lowers voter turnout, the impact of weather on U.S. election outcomes remains unclear. The most rigorous work to date found that precipitation benefits Republicans and suggested that Florida rains influenced the outcome of the 2000 presidential election, but a more recent analysis finding that precipitation only lowers turnout in uncompetitive election states calls this claim into question. Here, we reanalyze the 1972-2000 U.S. presidential elections with a focus on supporters of non-major party candidates, an oft-overlooked contingency. We propose that bad weather affects election outcomes not through its effect on turnout—as has long been assumed—but rather, through its psychological effect on swing voters. Specifically, we find evidence that bad weather increases regret aversion among supporters of non-major party candidates in competitive elections, leading some to instead vote for their preferred two-party candidate.

In other words, rain on Tuesday could swing some Gary Johnson voters to Trump.

Here is a page for Duhaime, and here is the home page of Moulton.  Both are from MIT’s Sloan School, and Duhaime is on the job market next year (I am not sure about Moulton).