I've found that most of the time, weather doesn't add enough interest to make it worth tracking.
Basically, weather is usually, "Gee. It is raining. Huh. Okay, we go into the lair...."
If I'm working a set piece, for which particular weather is especially important for flavor or plot, I'll include it.
This is aided and abetted by the fact that these days, I generally use an "upkeep cost" mechanic instead of having the party do detailed shopping. If they pay their upkeep, they have food, shelter, clothing, and gear appropriate such that the details of day-to-day weather are not much of an issue. If and when the characters go somewhere they don't have access to supplies or suppliers, then it may become plot-relevant, and I'll choose some tracking method for the weather and the resources used to handle it.