If your store doesn't suck you'll be fine. My store is in MN, so we're plenty used to having to deal with weather, but my store has never punished anyone who said they weren't safe to come in. We have a lot of high school kids who aren't experienced drivers and it would be really shitty to expect everyone to make it in when the weather is bad. This is somewhat analogous to areas that don't get snow very often--you're not experienced driving in it (or if you are, most other people are not) so it's just dangerous.
This entirely aside from the issues in Texas with no heat, power, water, etc.