With the cavalry, the idea is that the can hang stuff they're not using on the saddle. So when they are using their bows, the sword is sheathed, the lance is in it's carrier and the shield is slung over the saddle or something.
A lance, in particular, is a one handed weapon, and since almost no one can fight ambidexterously, a shield is something for the other hand. Same with the sword, really.
Clovis
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