I've been to a few private hunting preserves in Iowa and South Dakota. Around here, any extra tax stamp needs to be collected by the preserve owner. Usually, this is completed and purchasd when the hunt is over and the hunters are paying the final bill!.
As a side note, I've had my tagline for a couple of years!
On private preserves I'm sure that's true, but the Armstrong Ranch is a working cattle and oil operation and has been for at least 150 years. Most every piece of property south of I-10 has deer, dove, turkey, and/or quail hunting.