The Washington area has an interesting relationship with snow and it's winter precipitation counterparts (often referred to as the "wintry mix"). Being home to a large number of people from somewhere else, people are often confused. Why - in an area where there are food places everywhere would folks buy out the bread, milk and toilet paper at the mere hint of snow? Why do we close for snow? Or why doesn't the world shut down for snow? Where are the snow plows? Is it best to just drive faster in the snow? (No, by the way.)
So, my thoughts on this.
First, while the DC area typically gets some sort of winter precipitation each year, it is usually not in huge or even consistent amounts. This means that people do not get an opportunity to really hone their snow skills, and due to the aforementioned high number of non-native people this leads to problems. It also means that often when there is a budget crunch, stuff for snow gets cut because people don't complain about that until after the storm. (Schools and social services tend to get noticed quickly.)
So, while people from areas where it snows regularly find it peculiar, stuff tends to close for snow around here. (Not the places I work, but whatever.)
The bread, milk and toilet paper is strange since even during the ice storm that shut down the area for four days (I was off in college, but it made the news) the grocery stores were still open. But in some ways, it is almost self-fulfilling. You notice that everyone buts these things and you end up buying it because there won't be any left should you experience a normal shortage. And so on.
As far as how to drive in snow, I'm not sure that can be properly conveyed via blog, but no, faster is not better. Caution is good. And really, if you're not sure about your snow skills, try not to drive. Please.