For me during the winter if an ice storm just occurred and the roads are not clear, or conditions are just plain impossible outside like a blizzard at the time you want to run, then of course you might or will cancel your run. However, I have to say that the summer heat can be very taxing on the body. I ran for just over two weeks in Florida (while on vacation) form August 4 this year and I was just beat up after that. Therefore, while winter running can pose its challenges I must say that I have never suffered the worn out feeling to my body that the summer heat can bring.
In summery what I am saying is that, while there are physical hazards to winter running I do not find it debilitating on the body as the heat and humidity in the summer.
Running in the rain is not a problem for me, but in Canada, we do not have heavy tropical like down pours, at least not for long periods, and in the winter, it is too cold to rain. Mostly in Toronto where I live, we have very light rain that you can run in without a problem.