I would guess that in a society where everyone cycles, those that would usually be unable to cycle would gain the most from the exercise etc. I believe cycling in your 70s and 80s is relatively common in the Netherlands.
Isn't a wheelchair a weird single purpose vehicle, isn't a bike, or a car? There's nothing inherently wrong with being weird or single purpose, as long as it gets used.
'Around' 0c isn't that cold, gritting the road and putting on a coat would sort that. You're right there is weather that isn't great for cycling, just as there's terrain that isn't great for it either. I'm sure any global scale transportation solution is going to have its problems, no ones suggesting a one size fits all solution.