Let me add a few of other perfectly true statements:
- there are legitimate safety issues associated with driving in rain, sleet, snow, ice, fog, etc.
- there are legitimate safety issues associated with walking in rain, sleet, snow, ice, fog, etc.
- there are legitimate safety issues associated with sitting at home in rain, sleet, snow, ice, fog, etc. (see here and here if you don't believe me)

The question isn't whether there are risks: there always are, and inclement weather increases those risks. The question is how great are the risks relative to the importance of accomplishing the tasks at hand, and the risks and costs associated with other methods for accomplishing the same task. Risk is a spectrum, not an on/off switch.

We've had a couple bouts of freezing rains this winter (unusual here), and I would rate biking on studded tires as the safest transportation method available to me in those conditions. If I bought some ice grippers for my shoes, that would probably match biking for safety, but I don't own such things at the moment.

Fresh snow is the least fun riding conditions, and is one that I've come to avoid whenever possible. Most of winter is just cold and icy, though, which is much easier to handle.

Just to be clear: I'm not disagreeing with your choice not to ride in bad weather. It's the safety logic that I'm disagreeing with. If you don't like riding in bad weather, feel free not to do so. You don't need an excuse.