I've discovered (courtesy of some research, confirmed by asking Simon Chick) that all my Italian knights are on the wrong hosses, at least the wrong hosses for the late c. 15th. Apparently the pesky Italians almost invariably rode leather-armoured hosses, not at all like the metal ones that my current Italians ride. Also the pesky riders wore a distinctive sort of tabard called a giornea; who knew?
Essentially, I find that I need to convert 80 or so knights to form an entirely new army, and convert the existing 50 or so knights to become a different army of an early c. 16th nature. Such is the hard life of a mildly OCD gamer.
The upside is that the leather horse armour was richly decorated with heraldry and I can give them great big plumes. Simply ginormous plumes, in fact, from Mirliton in Italy. Onwards and upwards!