Hooves in the show work differently to that of RL hooves. They are flexible, for one, indicating softness. I imagine their undersides are quite soft, and the edges are just hard. Though even IRL, the frog of a horses hoof can be sensitive to touch, which is why a farrier must be very careful when shoeing them.
Either way though, their whole society and their use of magic doesn't make logical sense anyway, so I don't see how ticklish hooves are any more unbelievable.