To me, ir makes little sense that you can have 650 heavily armed and armoured horsemen, but not a single one with just a mount and spear.
Keeping and maintaining armour and arms is much, much more expensive then feeding a horse. Also, commoners could have plenty of use for horses, even in the capital. Horses were levied just the same as people, even if they werent warhorses: heavily trained and prepared mounts were the excepion, not the rule; you would see many more work horses in an army, repurposed from their usual farm or wagon duties, then war horses, much like knights were much fewer in an army then the levied pesants.
The only reasonable explanation would be that the horses not in use by the heavy cavalry were slain during the siege for food, but not even 50 of them could be spared? Then again, how could every single noble and richman in the capital have enough money to afford a full set of armour?
I fight for the rights of the light cavalry!
When can their glory start?
O the wild charge
they could have made!
All the world wondered
Where were they?
Honour the charge
they could have made!
Honour the Light Cavalry,
Noble fifty or so!