The hussars are based upon the painting and descriptions of the unit from Dan Schoor's fantastic site. The passage below comes from this site and explains the formation of the corps and its tactical uses:
Besides the Reiters, another type of regular cavalry was the Lancers. Lancers appear by 1662 in the Belgorod Corps (on the southern border of Russia). Two regiments were converted from Reiters to Lancers. These regiments consisted of 5 companies, each of about 100 men. One company in each lancer regiment was Reiter.
In contrast to southern units, in the Novgorod Corps (Northwest) a separate Hussar regiment was formed. It had different history from the lancers. The hussars were formed as a close combat unit in Reiter regiments. Russian hussars were a copy of Polish Hussars, but without "wings" and shields (I'm not sure in it, but I have not found any mention of wings and shields in this regiment). In 1662 a separate Hussar regiment was formed under Colonel Nikifor Karaulov. In consisted of 20 officers and 350 hussars in five companies. In 1673 this regiment numbered 417 men, and 465 men in 1679.
Hussars were armed with a lance (not spear) and pistols. They were protected by a light cuirass and Naruchnik (an armour protecting the hands). In the middle of 1670's Lancer companies were added to Reiters regiments in Novgorod corps too, but a separate Hussar regiment was retained.