True. Some of them don't seem to be wearing much armor either, though.
Does anyone have a source saying how horses were equipped for these things? 'Cause putting armor on them to protect them from the sticks and splinters would make a lot of sense, especially since speed wasn't as useful as it might be on the battlefield and since lower speeds are less likely to result in serious injury.
I'm not sure knights went out of their way to avoid injury. My understand was the whole fatal aspect was part of the allure.