Archer should hold the bow with his/her left hand
Your character in Morrowind is right-hander so he/she should hold the bow with his/her left hand.
Maybe Morrowind creators never shot a bow, but it would be nice to have some option in OpenMW to correct this nonsense.
#3 Updated by Gijsbert ter Horst over 2 years ago
The bow use and animations are horrible in both Morrowind and Oblivion (don't know about Skyrim), but I think it is beyond the scope of the project to fix it, since it would involve redoing original artwork instead of just a different implementation on the engine.
However for post-1.0 it would be interesting to make it possible to do the necessary work in a mod. Then someone could create a mod that provides bows held in the left hand.