Also the river crossing bridge battle sounds good to make a stand. Which province does this happen in?
From Kazar into both Kiev and I think Crimea IIRC, but you can find out by getting the province info screen open for Kazar and then putting your cursor in Kiev. The info screem will tell you what terrain the attackers will have and if there is a river.

Depopulating the provinces the horde emerges in does reduce their numbers quite a bit.

If you can hire any pavise troops are mercs they are real horde killers.