Dovid, you listed all the reasons – people will walk in the street, slipping on ice under snow, slipping on ice on the road. Falling in deep snow may be safer than on the ground but it is not safer than not falling. There are a number of people for whom falling is dangerous.
In many (most?) places it is responsibility of the house owner to remove the snow. So, this sort of makes it in your reshus that you allowed others to travel on – so then it is your “bor” to remove?
All of that might not have been a big issue in a shtetl 200 years ago – roads were hard to walk anyway and snow probably did not add much.