I ride in everything but a downpour, the kind of rain that sounds like a train hitting the windows of your house, and an electrical storm. I will show up to lead a ride, when scheduled, in any situation, and will roll out in everything but those circumstances. The length and route may be adjusted, but I don't get enough chances to ride that I can afford to sacrifice any.
The heavy rain issue is more about visibility to cars and presence of puddles than anything else.