If you jump into the water, from a "jump" point, while mounted your controls will get bugged.
The only way to unsheathe is to block. Swapping bars will sheathe your weapons.
I'm sure this is not an intended feature of the quest.
It seams to be cause by the quest update preparing the character for the effect after landing in the water.
When you approach the jump point again the character state is reset. Jump into water unmounted fixes the bugged state.