I have a lab who will go out in anything too, so if the weather is foul we do one decent long muddy walk (we are in rural village) for over an hour in the morning where he can get as filthy as he likes, then he gets rinsed off in the back garden, and towel dried in the utility room. I have a good coat, strong boots and was raised in the north of scotland where our parents would regularly dunk us in the North Sea to develop a strong constitution so a bit of rain is ok 
Later walks/school run will then be on lead, on pavement, so only paws to rub when we come in. He's getting on a bit so that seems to be enough for him.
We haven't had anything like the weather/flooding down south has had the last few days, so sending best wishes to anyone suffering as a result.