Living in Aus in a tropical/sub tropical zone, I agree with
enola and try to keep the run as dry as possible, wet dirt and/or mud + humidity is a breeding ground for bacteria and other nasties.
It is a constant battle to keep the run dry and the first site I visit each morning when I turn on the computer is the weather/rain radar
With our heat, I have shade cloth over the run which also keeps light showers from penetrating but have also fashioned a plastic rain cover for those more torrential down pours which we experience often. It takes me about 10mins to attach it, with a heap of pegs .. it is not pretty but it does the job. I am getting quite expert at attaching and unattaching, reattaching and unattaching depending on the weather. It cannot be left on for too long because if the sun shines for a while, the heat/humidity in the run increases ... sometimes it might be on for a day, other times only a couple of hours.
Using the deep litter method in the run, as
Ol Grey Mare has suggested, keeps my gals high and dry while lower lying ground outside of the run is wet.
We experienced a couple of floods last year and the smell afterwards was not pleasant.
As
tdepointe has suggested, I recommend plastic siding of some description; easy and quick to attach and remove; doesn't have to look good, just keep the rain out.