I would never willingly ride a road bike on the road even if it is drizzling.
Have I had to ride while it was raining, yes, due to sudden, unexpected rain showers.
The turns and the braking on wet roads (especially if there is a downhill), even when there is only a slight drizzle is too dangerous in my opinion. I can't speak for cyclocross bikes though.
2014 Liv Lust
2013 Specialized Fate Expert with carbon wheelset (sold)
2012 Specialized Amira Elite
2010 Santa Cruz Juliana with R kit and Crampon pedals (sold)
2011 Specialized Ariel Sport,suspension post,Serfas Rx Women's Microfiber saddle (sold)