The thing thats cool to do is to have the cats to actually attack the city. When there are bunches of troops there. The first 2 or 3 may lose but then when the collateral damage starts hurting them the cats start winning. You then get promoted cats which you can use to upgrade to cannons which start to be just city garrison killers. You run the cossacks to kill anything moving, the cats with some maces to take the cities.
Whats the point in going to all that trouble? dllotsofnumbers already pointed out that a cossak has a very good chance against a longbow with defence and 60% we may as well just use the cats to bombard the city defence down with the occasional suicide, instead of just wasting units.