I've driven Mike Duncan's three wheeler in near freezing conditions wearing my Barbour International jacket with a fleece underneath and was warm enough and will keep the rain off. Also looks the part being motorcycle related. You do need some decent gloves that keep out the draft and a hat that stays on! Goggles or clear lenses biker glasses to keep things out of your eyes....surprising how much rain stings!
I've a Holdens sheepskin flying jacket, chosen as its less bulky than the traditional Irving ones....and a bit cheaper. It's very warm but whilst fine in my 4/4, just too bulky in the three wheeler and would soak up rain like a sponge!