On days with light drizzle, I put my pants or skirt into a pannier, and wear tights or cycling shorts and a microfiber water repellent jacket on the bike (bright yellow for visibility). On days with heavy rain my better half usually insists on driving me to work, but if he didn't I'd put all my office clothes into the pannier and wear a non-cotton undershirt beneath the rain jacket. I wouldn't stay completely dry with this combination, but there would be enough warmth.