Winter road safety is very important and measures must be taken towards improving it. Poor winter road safety leads to more accidents and more deaths. This leads to higher costs for health care and insurance, but also increases the level of human suffering. Various jurisdictions have made advancements in this regard. For example, in Quebec, Canada, winter tires are required by law.
Even though people still have places to be and people to see during inclement weather, I think that the use of a motorized vehicle should be banned during something like a snowstorm. There are too many overly confident people in the world that think that they can do whatever they want on the road and they get others hurt and killed on the roads during this sorts of situations.
Many crashes happen every year due to the ice and snow after a winter weather pattern. Some areas are proactive about safety measures and send out plow trucks as soon as the winter weather starts. However, not all areas have the means to plow, sand and salt during or after a winter storm, and more measures can be taken to ensure driver safety in winter weather.
I don't believe that because the Ben Carson campaign had a crash during winter that it warrants for the state or city to change their whole policy on winter road safety managing. I am sure there are already a lot of regulation in place that manage snow removal and help make our roads safer in winter.