Yup,

done right, the horseman doesn't even need to swing his sword, he could just casually hold it out to the side, crash into a (loose-ish) formation, slashing everything he passes like the proverbial kid rattling a stick against a set of railings. The horse's momentum adds considerable force to the slashing action.

Of course, the density of the spear formation is supposed to stop them breaking in like this but it shows why archers etc are so vulnerable.

Cav impact obviously worked well for some time but the spear unit was developed to counter it. Faced with a wide spear line, Cav is left with nowhere it can make a real impression except out on the flanks where it meets... other cavalry. Depending on the relative qualities of Cav involved, most of its intended impact value has been evened out. Meanwhile, the infantry gets to take and hold ground as well as dictate where the Cav has to go, in order to be of any use.

Need I mention that pointy sticks (bayonet ends, to be precise) were still successfully baulking cavalry charges in the Napoleonic era?

If you've ever watched showjumping trials, you'll realise that, even now, a hedge or a few planks of wood at the wrong height will make a horse 'refuse' and even throw its rider.

By rights, frontal cav charge into spears ought to result in the Cav grinding to a halt, just short of being close enough to start fighting and thus lose no casuaties, thanks to equine common sense. Meleé should not start at all unless the spears actually advance by the few feet required to initiate contact.