Well, when Tink has to go, she has to go Right Now! There is no time to put on a rain coat.

So, out comes the umbrella! Fortunately there is good grass in the front of my patio so mud isn't a problem. I just take a dishtowel with me when we go out to dry her feet.
My Indy used to go the the closet when it was raining and bark for me to get the umbrella. He would not go without it. He'd sit in front of the door til he croaked but he would not get his head wet. Feet? No problem.