You guys know they invented the Lansknecht/hedgehog trick to deal with this kind of combat? The reason the halberd was invented (so I understand) was to provide a weapon for breaking up pike formations. Generally the idea was to assemble squares of pikemen with gunners in the middle - this was a classic tactic against cavalry, which is why people largely stopped using the old cavalry charge. Horses won't charge into an infantry square for the same reason they won't charge into a wall. If you don't believe in gunpowder, crossbows do just as well. Lastly, don't forget that great old unit, the horse archer! Mounted archers will make anyone's life miserable.