Stinz is actually playing officer, taking over responsibility for his men.
Notice the Colonel is talking about the tractability of horses when he’s sitting on a perfectly calm one. No, I tell a lie — Stinz has human in him. A horse can be a reasonable person, but humans are barely-contained chimps. You’ll see what happens in an emergency when the two are combined.
Gift really wants to keep the Halfhorse in his company; it’s a bit of a star on his cap. Bringing a new population into a condition for drafting would be very good for his career.