The military had its own set of rules when I was on active duty. If non-essential personnel were directed not to report, you did not have to use leave time. If you were considered essential personnel, you were expected to make your way in to the base.
After the military I worked for a large utility. If we arrived at work and were released due to weather, we were paid for the day. If we did not show up for work, it was unpaid or vacation time. We had "emergency travel cards" identifying us as working for a public utility and were allowed on the roads. Perhaps medical personnel have something similar?
Where I work now, if it is a telecommute day for me, nothing changes. If it is an in office day, if I have appointments, I need to make it to work or reschedule. Otherwise, I can change an office day to a telecommute. But I am the only employee with the telecommute arrangement. The others are expected to make it in to work or use vacation time.