Using dogs to hunt deer has always been very contentious in North America.
In the United States, the only states that currently allow the practice are in the old Confederacy.
And not all areas of those states allow it.
In North Carolina, for example, deer hounds are allowed in certain counties in the eastern part of the state, but it is both highly illegal and frowned upon in the western part of the state. The same goes for Virginia.
I believe the only Canadian province that still allows deer hunting with dogs is Ontario, though I stand to be corrected if I am wrong.
Using dogs to hunt deer was the most effective way to wipe them out, especially if the deer were running in heavy snow, which explains why it was frowned upon in the northern states and celebrated in the South.
The dogs that were used to hunt deer were sort of proto-coonhounds, beagles, and foxhounds.
These were the same sort of dogs that were used as “staghounds” and “buckhounds” in England.