LotR -- Book 1 - Chapter 05 - A Conspiracy Unmasked

[Essex]

A few things regarding the Brandywine (Baranduin)

Around 1700 of the Second Age, as stated in Unfinished tales, Sauron was driven away by Tar-Minastir and his forces after great slaughter at Sarn Ford (the crossing of the Baranduin).

The ringwraiths fear of the water could stem from here. (But then they did use the actual Sarn Ford crossing to reach the Shire, so this is not concrete evidence).

More on the river: regarding people who seem to have been driven out of their homesteads by the Numenorians

and the native folk that survived fled from Minhiriath into the dark woods of the great Cape of Eryn Vorn, south of the mouth of the Baranduin, which they dared not cross, even if they could, for fear of the Elvenfolk.

Again we see (people this time) afraid to cross the river Brandywine.

I think it could just boil down to the fact that black rider and horse were not able to swim across the river, but could use Sarn Ford, which just required ‘wading’.