As a general rule you do not run your heavy ships up rivers at all. Usually not the medium ones either. I mean, why would you? River province (and coastal provinces for that matter) are assumed to have lots of ships baked into province/holding levels. You don't need those ships to ferry troop across river or carry supplies. And knowing that I would rather have my galleon near the seas, where it is useful, than up some river where all sorts of bad things could happen.
A couple of exceptions come to mind though; take Aerenwe. Calrie is up-river and ship have to move up and down river to get to/from the sea. But then again Calrie is classified as a coastal province so the point is sorta moot.
Light ships travel more freely on rivers. A staple of Rjurik raiders is rowing inland and making raids. Rives you access to a lot of Cerilia that way. Not so common these days though. The Vos have tried to take up that tradition - but only of on the Dragon Coast, so no worries.
