I've never met a drowned rat, personally, nor have I any wish to do so, as drowned rats tend to be, er, no longer alive.
Fortunately there is an idiomatic meaning ... which I know well having been caught in an October thunderstorm.
To be absolutely sodden after getting caught in a downpour. Never nice, really
Use in Normal SpeechEdit
To explain why they have to change clothes.
"I'm sorry, I'll have to change gear - it's soaking out there! I'm like a drowned rat!"