Cannons made a big impression when they were introduced in Eastern Europe. At first, they merely scared people and terrified horses, and did damage. The scaring of horses was good. You see a lot of cavalry warfare. That, and actually harming horses would certainly take the moxie out of pretty much anyone that thought to belabor you with daring cavalry tactics, which would be anyone who was anyone in that time period in eastern europe. Bandits, other lords, howling steppe raiders and cossacks, the list goes on.
It would be ideal to get something like canister shot, as you can get an effective range of around 400 yards, and your mongol style composite bow is recorded as having made shots at 500, but not reliably.
If you supported a decent cannon with good powder, it would make a mess of any given group of anything. You could just have footmen and archers and crossbow men hang around, and take shots at anything the cannon didn't get.
If you could manage to make a battery of them, and keep the crews relatively safe with say palenquins or what have you,and support as above, it would be just brutal. Recall what fully developed guns of this sort did at Gettysburg.
Granted, you wouldn't get anything as good as a Napoleon Gun in this setting, but you wouldn't need it so much, especially if you were using canister, or plain old scrap metal and rocks at a pinch closer.
If you put guns like this on walls, good fucking luck for anyone messing with you. "Oh, you wanted to assault my wall? Enjoy your entire attack being turned into hamburger".