The classic trail rule for riding in the rain is to roll directly through the middle of standing water, rather than around it, to avoid widening the trail. Some ecosystems are more fragile than others and, depending on the soil and plant life where you ride, those wide spots surrounding puddles might become permanent.
Apart from puddles, riding in clay-based soil can leave tire-wide ruts in the trail that set in like cat paw prints in concrete once the soil dries, destroying any work your local trail builders did to smooth the tread. In this case, trails are often closed during wet weather, and sometimes for up to 72 hours following rainfall.
In places like Scotland, Ireland, western Oregon, western Washington state, and numerous other rainbow capitals, riding in rain is the only option. Trail builders in soggy environments have to know a lot about drainage and bridge building. Having lived in Portland, Oregon, I can say that being soaked and muddy on every ride grew old, while it also forced me to learn valuable wet weather riding and bearing replacing skills.