Query - infantry in column surrounding cavalry

[BigDuke66]

Just some historical background to it, from "Napoleon, His Army and Enemies":

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Only few times the infantry
actually attacked cavalry.

1.
In 1811 at El Bodon, British 5th Regiment of Foot attacked French cavalry.
2.
According to l'Houssaye, in 1814 at Craonne, two regiments of Russian infantry attacked French dragoons commanded by General Grouchy. The boldness of the infantry were enough to drive back the dragoons on to the battery which they had just captured. Grouchy was wounded.
3.
In 1809 at Aspern-Essling, "Instead of losing momentum by ordering a square, he [Saint-Hilaire] commanded the trusty 105th Line to face to the flank, told the drummers to beat the pas de charge, and advanced against the enemy horsemen. Infantry charging cavalry was thing rarely attempted. It demanded great resolution. ... The 105th met the challenge and drove off the startled Austrian heavy horse." (Arnold - "Napoleon Conquers Austria" p 70)
4.
In May 1813 at Diehmen, allied cavalry attacked the square of French 52nd Line twice. The 52nd and 137th Line reformed into columns, and advanced at the "pas de charge" against the Russian cavalry. The cavalry faced with the startling and unusal situation, withdrew. (Nafziger - "Lutzen and Bautzen" p 201) Other sources mention the 53rd instead of 137th.
5.
In 1812 at Borodino, the battalion columns of (Russian) Ismailovsk Lifeguard Infantry Regiment received French cuirassiers with volley and then attacked with bayonets. Officer Shimanski of this regiment doesn't mention the bayonet charge, he wrote that only some soldiers left the ranks and fired at the backs of the fleeing French. The Russian 'Pernau' Infantry Regiment repulsed cavalry attack and then itself charged the cavalry with bayonets. Unable to catch them some men in the front rank threw their musket with bayonets as javelins at the backs of the cavalrymen ! (Zhmodikov - "Tactics of the Russian Army in the Napoleonic Wars" Vol. II)
6.
In 1813 near Katzbach, the French IV/34th Line "found a force of Prussian uhlans had charged into and captured the park of the French XI Corps. When only about one-sixth of their muskets would fire because of the day long rain the IV/34th Line charged, in a battalion mass, against the cavalry, drove it away, and recaptured the XI Corps park. They do not appear to have suffered any appreciable losses." (Nafziger - "Imperial Bayonets" p 42)
7.
In 1814 at Vauchamps, two companies of the Prussian Silesian Schutzen (240 riflemen) found themselves with a single squadron of Polish Guard Lancers sitting on their line of escape from the disaster that was befalling on their brigade. The Schutzen formed a column and charged forward cutting their way through the enemy cavalry.
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So there are examples that infantry can handle cavalry roughly, but if 400 men cavalry are running right into such a mass of infantry(4200) it's there own fault if they loose more than just some feathers.

You only use cavalry if the circumstance are beneficial to you, in an active role only to finish off an already retreating/routing enemy, in a passive role just to threat the enemy to force him into squares that are then soften by artillery fire(horse batteries come handy here) and kicked by a charge of a superior infantry force.
The only other reason to use cavalry is if you're desperate.