Your are correct. Deers and rabbits run lot faster than a potato tree.
Lots of rodents about. Porcupines are easy to catch. Rabbits aren’t that fast...but they corner really, really well. I chased a few jackrabbits coming home from the Airman’s Club at Lowry AFB. If you can hit them with s stick or a stone, and had multiple hunters, you could even the odds.