Nothing to Do with Caesar
Hail Day is a lot more fun than Sleet Day. Unfortunately (sorta), it's also more rare.
I could probably count on two hands the number of times I've seen hail in person. Ever.
Most of the hail that I have seen has been the pebble-sized stuff. It's hard to remember, but I may have seen quarter-sized hail a time or two.
I don't think I've experienced a hail storm that has actually caused any damage that needed repair, at least, not to stuff I owned.
There is an account in the Bible where a hail storm killed more men who were in battle than were killed in the fighting itself. That must have been some hail! I wonder how large the hailstones were.
As with Sleet Day, you might have a hard time celebrating Hail Day in the proper, formal way. You might need to find an alternative.
Even though (as mentioned briefly above) this day has nothing to do with Caesar, in a pinch you could greet everyone with a "Hail!" instead of a "Hello!" today.
It might be interesting to see if anyone notices.