My thanks to all who replied.
David, your Waterloo story leads me to speculate: The Prussian King was present at Auerstadt. When it became clear that the battle was lost the King ordered the grenadier battalion forward to cover the retreat of the left wing. Somewhat later it's indicated that another battalion retreated with the King's baggage .
It's possible that the "handpferden" being guarded by the grenadier battalion was, in fact, the King's baggage and that this duty taken over by another battalion when the grenadiers deployed. That would explain why an elite battalion was apparently "wasted" tending horses.