As I write this a tropical storm is passing over Orlando and has turned out to be milder than expected (good) and authorities have taken steps to cancel school and ask people to stay at home if at all possible just in case (also good in my view). Yes, you can drive in 40-50 mph winds if you have to, but why take chances if you don't have to? Let the first responders work on important stuff, not having to come bail you out because you just couldn't miss a day of work.
An old friend emailed to say his employer was not closing for the day or even giving employees the option, because the winds wouldn't be that strong. In this case the winds are lighter than expected, but just as easily could have gone the other way. It's not just employee safety that's an issue though, local schools are closed - what do single parents do on 4 hours notice that they need a sitter for the day? Does the employer let them bring the child to work? Is this really taking care of employees?
Some businesses need to be open as long as possible during these events - grocery stores, gas stations, home improvement, and of course police/fire/medical staff. Part of the job for all of them, but even for them it's useful to remember that they'll be more effective if they know what will be expected of them well in advance and you help them take care of family in whatever ways you can.
For many businesses it's about lost profit more than anything. Close for a day and you miss out on 1/20 to 1/30 of the planned monthly revenue. Miss your numbers and your President/Board start getting itchy. There's going to be a few days a year where stuff goes wrong, from storms to bad software upgrades!
And what about us might ask, we run a training business here in Orlando, what steps do we take? Typically we follow along with whatever the local school distict does. If they close, we close. As I write this I'm sure that it's safe enough to be out and about, but at 7 am I couldn't have guaranteed that for the day. Safety of our students come first - not out of fear of some lawsuit but because it simply should come first. We also try to be good citizens as part of our community, and if they want us off the roads, we'll do that if we can. Students are stuck at their hotels of course, not the most fun venue, and we call to check on them to be sure all is well. Easy for us because we charge by the class? Our primary plan is to make up the hours after the storm passes. Should that not be possible, we'll refund them a pro-rated amount based on lost hours. It's not perfect, but it's a decent compromise.
Personally I don't find it too hard to decide what to do in these situations, I want to treat clients/employees the way I want to be treated, and I'd prefer to be at home with my family. Work in important, but not that important.