[wffurr]

Are you speaking from experience? I am. Proper equipment solves for rain and snow.

Crashing into a pole with your kid on board? A) don't do that? B) you'll all be fine as the speeds you should be riding with children along.

Not sure what you mean by a "bike buggy", but bike-mounted seats do provide protection against falls, and bike-towed trailers are essentially immune to them. Longtail cargo bikes put the children in the rear and have a bar that also protects during a fall. Box bikes are very difficult to overturn completely and also provide protection.

If you want to talk safety records, cars are by far the worst. They're extremely dangerous for the occupants and everyone around them.