I graduated in 1998 and to be honest, I really cannot remember a bad snow since then. Before that though while I was in nursing school I think each year we had a blizzard. It really depends on where you work. In the years when it was needed the nursing homes and hospitals actually sent employees after you in 4 wheel drive vehicles or sent the national guard after you.

I am pretty sure that every hospital I worked at would let you stay if it was bad for free and would provide you with scrubs to wear.
I no longer work in a hospital but my current employer will put me in a motel if needed and when I worked for an insurance company a few years ago, you were able to get a hotel room on the company card along with a free meal, no questions asked.
I have pretty much though always had a 4 wheel drive vehicle not so much that I can get there but that I can get home
It really does depend on your definition of "bad" though. I have drove home many times with a few inches on the road but I always had a nice vehicle I could depend on and I went slow. I grew up in Southern WV so driving back and forth to school and my job, I had to drive on bad roads quite a bit.