At the very least, I'd discuss this with the department chairman and the dean. On the face of it, it's pretty strange. I'm assuming you don't live where 2" of snow is a minor matter.
I've taught evening classes in blizzard country a couple of times (before cell phones became so common), and I knew some of my students would be coming from up to 100 miles away. My announced policy was that I'd be there, but if there were blizzard or ice storm warnings out, people were to call my office phone, listen to the recording, and leave a message -- I know I called off class at least twice, even though the university was technically still in session. Got a few on-campus students or close-in students both times when I called off class... both times, there were papers due in a couple of weeks, so they and I reviewed what they had done and I made some suggestions for further places to dig for information -- so we hadn't wasted their time, and I ran makeup sessions the next week for the students who hadn't come. But I wouldn't have dreamed of making someone sit on their thumbs for a couple hours.
IMHO, placing "showing up and staying" over real concerns about safety shows poor judgement on the part of the person doing the demanding. Classes are not life-and-death or keep-the-infrastructure-going situations. And I'd bet the school's lawyers would be sweating bullets if someone was injured going home after such a policy.
And taking a cell phone call before dismissing class? Just plain rude.