Proposed Canon
First Mentioned: IPTSF Text 3
Quarterhorses are likely made of US 25-cent quarters, or something similar.
They might be a form of Golem, potentially being made by a Moneymancer. If so, their presence in Goodminton would suggest they may have had a Moneymancer at one time, or hired one, or that one or more of their cities could produce them (which would lend credence to the idea that cities can produce golems without a caster of the relevant discipline on their side).
 Real World References
Quarterhorse may be a reference to a breed of horses known as quarter horse.
In Goodminton, Wanda observed how "stalwart knights led alternating charges at one another on quarterback, then on nickelback". This may be a reference to quarterback and nickelback - player positions in American football.