Many accounts of the battle of Zama seem to be a stalemate of infantry combat until Scipio's cavalry force attacked the Carthaginians in the rear. I know the Numidians were very skilled and expert horsemen. However, my understanding is their armament was very light; small horses, a handful of javelins, little to no armour. I don't understand how they were the pivotal factor in the battle, especially as by this time they would likely be tired and/or running out of ammunition. I feel as though they wouldn't have much effect on a larger mass of infantry.
The effect of cavalry is primarily psychological. Keegan documents this in The Face of Battle, and I've corresponded with Robin Lane Fox (the historical advisor for that terrible Alexander movie) who corroborates the point. Basically, horses won't charge what they perceive as a solid barrier, but if the infantry scatters, the perceived barrier disappears and the cavalry can have at it. To that extent it doesn't really matter what the Numidians were equipped with.
If you're in an ad hoc infantry block, you can hang together and defeat a charge of cavalry. But you have to have absolute trust that the other guy next to you isn't going to run, otherwise you run first. If the infantry block breaks, it's GG.