A stripped coat is naturally pretty weather proof anyway - Cara (clipped) gets much wetter faster and so feels the cold more than Mo who has a good wire coat on her as the wire hairs keep out the wind and rain well. Most of the time my two don't need coats, especially Mo with her natural anorak. The only times they wear one is when they are stripped bald to keep the chill off and they wear a coat out on walks then. I've tried putting a t-shirt on in the house but Mo removes them and they don't normally survive as she uses her teeth!
You may want a lightweight waterproof in case of really heavy rain but I tend to delay walks in such weather if I can so they are not essential.
Cara and Mo, two black mini's and Molly a black & white Heinz 57 all served by Elaine, the cook, poop picker, and chief toy thrower.
I live by the Mini Schnauzer code; when in danger or in doubt, run in circles, scream and shout!