Well two things. One, the horses that were in these kinds of charges are not the cute little ponies that you take your child to on the weekend. These were horses bred over hundreds of generations for the express purpose of war -- they were (and are where they still are bred) larger, faster, and meaner than other breads. Two, I think you're rather underestimating the sheer lopsidedness of how much damage a horse can do versus flimsy meatbags like us.

Yes, those men in a giant mass of spears are pretty darn impressive. They would throw a massive wrench in terms of stopping the momentum of a cavalry charge, but would it be enough? Think of it like this -- a war horse would weigh roughly 550 kilograms we'll say. Moving at 40km/h (~11m/s) that's impacting a force of 33275 Joules. That's about 23,000 ft/lb's of force. That is absolutely insane. That is enough to knock someone out just from the impact of the horse. And it's not just one horse, we're talking about hundreds of horses moving tightly together operating, functionally, as a single mass.

So, we're at a crossroads here. If the infantry body is large enough and holds its ground, they are a tightly packed mass each of let's say 70 kilograms with spears/bayonets sticking out. All those bodies tightly packed together operate functionally as a single bodied mass weighing thousands of kilograms together and firmly planted. And, in that case, they can hold off the momentum of the horses in all likelihood. All you essentially need to do is break the first line or two of the charge and the rest run into the stopped rear ends of the others in the front and the entire charge dissipates.

However, once that mass begins thinking as individuals, it loses all its clout. It's no longer a single bodied mass, it's a bunch of squishy individual 70kg bodies. And those 550kg horses are going to win every single time -- it's just physics. And that was mostly the purpose of cavalry -- to strike infantry which were either broken from formation, or were heavily wavering and were ready to break. When cavalry did engage cohesive infantry directly it was usually at their most vulnerable positions -- the sides or rears for instance. This is why in the 18th and 19th centuries, riflemen would form infantry squares such that they couldn't be hit from a 'blind spot' so to say. And it's why in the 16th and early 17th centuries, when armies were literally giant squares of pikes moving as a giant square of death, cavalry adapted to a lighter form based on harassing at range with pistols while the use of on field light artillery flourished.

Yes, there are times where cavalry charged right into a wall of spears head on that were cohesively formed and still won. This speaks more to the quality of the cavalrymen more than anything else. In the case of the Winged Hussars, their cavalry would be near fully armored (yes, the horses themselves I mean) along with those riding them. The cavalry would also be carrying unusually large lances, ones that let them at times strike the infantry in the pike line before said infantry could strike the horse first.

Adding to /u/elos_ 's post, based on prior post, I'll talk about the early modern era in western and central Europe as close-order tercio style infantry rose to prominence. There was not yet the socket bayonet that allowed a musketeer to also provide turn his musket into a pike-like instrument, so infantry units had both pikes and handgunners organized in squadrons to support each other. This is exactly what the cavalry tried to exploit. Charging straight into a mass of pikes isn't an option so cavalry units had to exploit "gaps" in infantry defense.

Reiters / Cuirassiers / Caracole

In the 1500s-1600s, Reiters / Cuirassiers / Caracole cavalry were useful in as far they could harass arquebus & pike formations, at a time when musket fire rate and accuracy were quite poor. Cavalry could not charge head on into a block of pike, so the role had to be adjusted.

In a pitched battle, Cuirassier units harassed enemy formations to break up their cohesion, and then allow friendly infantry to exploit gaps. What does it mean "gaps"? Squadrons of pikes and shot tended to be deployed as such. So the concentration of shot are on the sides of the pike block. Which makes sense because if two pike blocks are to engage, they want their friendly shot squadrons to pour fire from the flanks. The Reiters would attack, in caracole, at the exposed pike block. If the shot squadrons tried to move forward, they themselves may be exposed to the opposing force. Or, the Reiters would harass the sides of the shot squadrons. So there was a lot of coordination at brigade and squad level. Such was the state of pike & shot coordination in that period, up to around 1700.

They would charge at disrupted units, or assist friendly units from the flanks. Cuirassier armor could withstand arquebus fire even at shorter ranges, and Cuirassiers tended to be better trained and disciplined than arquebusiers. As a result, arquebusiers tended to fire their guns at too long a range neither to be accurate against formations of Cuirassier nor to penetrate their armor. These reiter units had good armor and carried weapons for melée, so they were flexible.

Around 1630, Gottfried Heinrich Graf zu Pappenheim famously tied down an entire Protestant army using a small force of elite Reiters in the Westphalian theater of the Thirty Years' War, using his mobility to strike at unexpected weak points.

But over time, as musket improved in accuracy and fire rate (especially thanks to the switch from matchlock to flintlock), and as infantry formations tended to be linear and with less emphasis on pikes, the role of heavy cavalry shifted and the Reiter became unpopular.

Harquebusiers and Dragoons

These were largely developed in France as mounted handgunners that used horses for mobility. German units started to copy them in the 1600s, and the German dragoons fought either dismounted or from horseback. They were otherwise equipped like infantry musket units and were not armored although they carried swords.

Harquebusier cavalry were mounted handgunners carrying the lighter arquebus. They were initially partially armored, but the level of protection declined over time. They often also carried pistols and were reported to use first their arquebusiers while mounted, in a manner similar to the cuirassiers' caracole but from a larger distance, and then switch to pistols and swords when the enemy infantry formation becomes disrupted. Ideally, they would be supporting the heavy cuirassier units both through harassment and assisting in assault. However, they seemed to have been considered limited in success as they would refuse to close in. Wallenstein notably disliked them.

Organizationally, these units were somewhat confusing, as they were often counted among infantrymen, with the special note that they had horses and thus had higher pay and were given fodder.

Others

There were also the Polish winged hussars, but they are outside my area of focus so I'll let somebody else write about them.

Hi, you may be interested in a few earlier responses on cavalry charges

• How is it that such an unwieldy animal such as a horse was so effective in combat, especially when used to charge heavy infantry formations. - /u/britainopplsnerf discusses the effectiveness of horses; /u/Rittermeister and /u/Second_Mate talk charge tactics

• How do Cavalry charges actually work? - /u/DonaldFDraper and others discuss 17th/18th c; /u/MI13 looks at earlier eras

• Cavalry charges, in real life wouldn't the people in the back of the unit smash into the people in the front of the unit? - /u/Georgy_K_Zhukov, /u/Rittermeister and others describe charges, and include a few video illustrations

• Why was cavalry so deadly? /u/Aethelric , /u/TheGreenReaper discusses the value and effectiveness of cavalry

So how deep of an infantry formation is necessary to stop a cavalry charge, and how long do the spears have to be?

In the Renaissance and Middle Ages armies had massive blocks of pikemen up to 50 men across and 50 men deep armed with long pikes up to 20+ feet in length.

But during the Napoleonic era, hollow infantry squares would be only 3 to 4 men deep and armed with bayonets on the end of muskets, maybe 6 to 7 feet long.