If you can drive in the fog you can bike in the fog, you just need powerful lights. You can get a rear red light from BLT, I believe it is the super doppler dx, it is as bright as the law allows. Just as bright as any tail light on a car. You can also get extremely powerful front lights for your bike. Is is the safest way to travel? Well, I don't think it is any more dangerous that driving.

Hope this helps.