I don't ride the first day it rains but I'll ride if it has rained for 2-3 days. The first day the roads are pretty dirty and you get crap all over you. The next couple of days after the road is a lot cleaner. After a rain ride, remember to clean your bike. You'll need to drive off your drivetrain parts and oil your chain so it doesn't rust.

A lot of people have a beater or winter bike. I use a cross bike which is great for fire roads and wet weather since I can install larger tires and fenders.