All of the weather theatrics add to the drama of the story, as well as liven up the setting and convey a feeling of Wyoming-ness. But in addition, I think it is a custom of Western writers and artists to treat the weather as another character in the story. They use it to echo, underscore, or complement the action/mood/feelings. Ang Lee also said that since he didn't use narration to tell what the characters were feeling, he had to do it in other ways, through setting, props, atmospheric effects, etc.
I love the way the general wetness of the story/movie works with the electrical currents. There's a technical term for this in my line of work called "electrowinning." You run an electrical charge through a solution, and there is a chemical reaction which results in you "winning" whatever you were seeking to gain: gold or another type of metal. What a metaphor!!