I get it. We have a reputation as a "party school". Three years ago there were snow days and the students went wild. You do not want that to happen again.
However, that is no excuse for the way you are currently treating your students.
I am aware that it could be worse. We could be somewhere in North Dakota or Minnesota with three times the wind chill we have here, but still. Even the our university police department has advised against being outside. You, as the University, sent us an email about how we should winterize our cars, and pack snacks in case we get stranded, because being outside is that risky. But you ended that email by telling us that classes will still be held.
In as little as half an hour outside, your students are risking hypothermia and frostbite. Note that some class buildings are over half an hour away from each other. If a student is lucky enough to have a car on campus, you have to factor in the fact that unless they live on a main road, they are going to be sliding all the way to their destination. For those without their own vehicle, the main form of transportation is closed indefinitely, because it is too cold for it to function. This leaves your students to stand at bus stops for who knows how long, because the busses are stuck in traffic from the terrible roads, if they are fortunate enough to not have to walk there.
Some students have the ability to make, the very understandable decision, to skip their classes for the day and stay inside to avoid the miserable weather we are having. I am jealous of those students. Some students, like myself, have three hour lectures that only meet once a week, and therefore are unable to skip without jeopardizing our grades. So you leave us with either risking our wellbeing, or risking our GPAs.
Do better. Think of your students that are not from this area and are not used to these temperatures. Think of something other than an irrelevant "party school" reputation.