Everyone has to make their own call depending on their circumstances and comfort level. However, I find that most non-cyclists greatly over-estimate the risks of riding on roads. These same people think nothing about the dangers of DRIVING on roads, but think cycling is fraught with dangers. I personally feel less safe when I drive to work -- most of the time -- because the traffic is much worse and faster on the roads that I drive to work on. In contrast, my bike commute route is mostly on roads with less traffic and slower speeds.
That said, I usually don't bike commute on days when there is heavy fog, rain, sleet, snow, ice, etc. My commute is about 31 miles round trip and takes 2:15-2:30 depending on the wind, other weather conditions, traffic and number of red lights that I catch. I simply don't enjoy bike commuting enough to extend that trip any longer, plus the traffic is bad enough on some roads that I don't want to risk it in heavy rain, fog, snow, etc. We don't get enough snow and ice to make it worthwhile to use studded tires, and I failed miserable the one time I tried to ride in snow/sleet. Perhaps if my commute distance was shorter I might be willing to tackle the snow, but there's no way I'm going to ride 15-16 miles each way under those conditions. It would simply take me too long. Plus, we get such little snow/sleet around there that most people don't know how to drive in it and there are literally hundreds of accidents. It dangerous to even drive in it.