Here's the problem with you internet experts. You stated:
Hounds have just as much right in the woods as any game animal.
And then you cited Wisconsin State Statute 174.01 in support. It does not say what you think it says.
What you should have done is keep reading and you would have found:
174.042; Dogs running at large and untagged dogs subject to impoundment; penalties.
(1)Dog running at large.
(a) Except as provided in par. (b), a dog is considered to be running at large if it is off the premises of its owner and not under the control of the owner or some other person.
(b) A dog that is actively engaged in a legal hunting activity, including training, is not considered to be running at large
if the dog is monitored or supervised by a person and the dog is on land that is open to hunting or on land on which the person has obtained permission to hunt or to train a dog.(2)Untagged dog. A dog is considered to be untagged if a valid license tag is not attached to a collar which is kept on the dog whenever the dog is outdoors unless the dog is securely confined in a fenced area.
(3)
Dog running at large or untagged dog subject to impoundment. An officer shall attempt to capture and restrain any dog running at large and any untagged dog.
(4)Penalties. If the owner of a dog negligently or otherwise permits the dog to run at large or be untagged, the owner shall forfeit not less than $25 nor more than $100 for the first offense and not less than $50 nor more than $200 for subsequent offenses.
You lose, internet lawyer. Wisconsin state law disagrees with your position that dogs can run free like a deer.
I didn't waste time looking up whether I could shoot a dog chasing cows on my property if I owned any in Wisconsin (which would be cool because it's beautiful up there). Also, I wouldn't care what the law says anyway. My place. My rules.