We are flying in the same day too - flying from DC to Orlando and arriving at 9:30 am for our cruse that leaves on 29 Jan. Like you, I didn't want my son to miss any more school! I am tying this cruise in with a 2-day holiday so he is only missing three days. I know some people say "what's one more day" but even for my son in 3d grade that is probably a minimum of 2 more hours of work to make up on vacation!
We don't usually have super severe weather, but last year we were HAMMERED. My plan is to pay pretty close attention to the weather. At least for us, they start telling us about major snow storms coming 3-4 days in advance. Then I will call and try and get an earlier flight or jump in the car on Thursday and drive down. We are fortunate to have that option - I can be in Florida in 13 hours (with traffic) and am pretty sure if I can make it to North Carolina, it would be smooth sailing from that point. We also are lucky in that there are three airports servicing DC as well as the auto train that stops just a few miles from my house, so we may have more options. Even with flights, there are direct flights leaving every hour (we are on the first one of the day).
No use worrying. I have purchased trip insurance that covers missing the cruise departure because of weather which is about all that I can do! If we have the snow that we had last year, even people leaving 2-3 days ahead would have been snowbound. They just would have been spending three more days trying to get out!