I have reached the conclusion that in a typical British autumn/winter, you can only ever be two of the three. All three at once is not possible, not if you need to go outside at any point, and doubly so if you have small children and/or dogs to wrangle so can't carry an umbrella.
I prioritise warm and dry over style these days (was a different matter in my youth!). I did the school run and (brief) dog walk this morning in wellies and my new Barbour coat. I got it vastly reduced in the middle of the summer heatwave and I'm so pleased I did as it's fully waterproof and keeps even my Raynauds-riddled carcass toasty warm, but I'm under no illusions that I look stylish.
Underneath I'm wearing a blue cashmere jumper and leather-look leggings, which I don't think are very stylish either - I'm aware we're meant to be wearing wide leg or bootcut now, but they're no good in the wet or under wellies. The leggings are at least wipe clean when the dog gets me mucky, and at least I'm warm and comfy. Swapped the wellies for my sheepskin slippers when I got in, too.
If you have cracked the warm/dry/stylish trifecta, I'd love to know how!