I think the worse is rain in hot summer. You'll end up soaked whether you cover or not. Winter rain is OK, you just need appropriate clothing. Source: I cycle during the whole year, and sub-zero temperatures are not a problem at all (for a couple of weeks at most in my latitude, but still), even if it rains.
I disagree, it's a very real annoying problem to dress your whole body in both warm and waterproof clothes, and even if you like it, most people don't. And it is objectively, relatively, much less convenient and much less comfortable than the alternatives of a bus/subway.
> much less convenient and much less comfortable than the alternatives of a bus/subway
This is quite subjective... For one, I've commuted by bus+subway for most of my life, in three different European cities (Lisbon, Barcelona and Paris). Two years ago I had a sort of epiphany looking at the bike lane that followed the same path as my crowded bus. I bought a bike, in order to "try" the bike commute, and I've never looked back since. Even some days with hard weather, I prudently walk to the bus stop, and then say "no shit" and walk back home to pick my bike.
Thus I politely disagree with you that it is "much less convenient", at least for everybody.