lugh
I agree that it does not seem to add up. Based on surviving skeletons the Classical Greeks (circs 4th century BC) had horses that averaged 13 hands high, and those were considered unsuitable for serving as the mount for a fully armored Persian (etc.) cataphract. So after 1500 years of breeding heavily armored cavalry were riding horses only marginally larger than classical Greek horses that were considered largely unsuitable for the roll?
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