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.
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.