I'll find out how I'm prepared for cold rain tomorrow morning. It'll be in the low 40s and raining.
I'm going to wear tights & some pants (not really waterproof), t-shirt, thermal shirt, windbreaker (with hood under helmet), beanie under hood, cheap rain jacket, and leather gloves. It's all I could get together in a hurry on a budget.
I'm riding the recumbent, which has fenders, and my SPD shoes. My feet will probably get cold and wet. I'll have a full change of clothes once I get to work. Luckily it's supposed to be light rain in the morning.