Yes, please wear closed-toed shoes for any axe throwing session. Closed toe shoes are required for your safety. If your axe slipped out of your hand, we want your feet to be protected. Wood chips also fly off the target, so you could easily get splinters if you do not have on closed toe shoes.
We also recommend wearing a comfortable shirt. You will be making overhand throws, so test if your shirt allows you to do this. You do not want to wear one that is too tight to constrict your motion.