We can on private land just not on public and we actually have a deer dog training season.
What we do is we send the dogs out after the deer and they herd them back towards our direction.
For me though my favorite time is the training season. To see the dogs do waht they were trained to do so well and to hear the constant bay of the hounds (and tytus) is just Amazing. I cant imagine anything that tops that. I don't go for the deer its just breathtaking watching the dogs work knowing you trained them and that they enjoy it. (sorta the thrill that a agility or obedience trainer gets from watching a dog in a show or trial) To me its a whole lot more though because it involves the dogs thinking and actually doing whatever it takes to get this unruly animal to come to you.
Heres a article explaining it somewhat.
Traditionally the deer dog was a long-legged walker, a blue tick, or a redbone. Today this breed of big dog has been mainly replaced by the beagle or the short-eared black and tan. These dogs are smaller and cheaper to maintain. They do not eat as much and they will stay in a smaller pen. These dogs are slower, too. They will not run as far and they are easier to catch at the end of the hunt. The driver, the one who owns the hounds, picks a place to hunt and assigns everyone a location. A stander is a hunter with no dogs. This hunter is put in a designated deer-crossing, a place where the deer are known to cross. Deer crossings may be dirt roads, old logging roads or just a spot in open woods. The driver walks the dogs through the woods to jump a deer and run it to a stander. The deer will lie in the woods, and unless the dogs stumble across it, the driver could walk right on top of the deer and never know it was there. The odds are mainly in favor of the deer. Only a few of its exit routes may be covered by the standers This opens up many windows of escape for the deer. The old belief that a deer is always ran down and caught by the dogs is not true. The deer have no trouble staying in front of the dogs, and since no two deer run alike, the drivers have to be ready for anything. The deer runs as far out in front of the dogs as he wants to unless he is hurt or injured severely. Even then, the dogs bay the deer and keep it surrounded until the hunter gets to them. They do not attack the wounded animal. The deer eludes the drivers many of the times. They run way out in front of the dogs to listen and smell for danger. After they get out of the designated hunt spot most of the drivers spend good quantity of time looking for the hounds. Some hounds will return to the location they are cast from. However, some hounds may run forty miles or so before getting caught. If the hound is wearing an identification collar, the person who catches the dog may notify the owner. The kill of the deer is only a minor part of the thrill the hunter gets from dog-driving. Most dog hunters enjoy the race of the dogs they have trained and raised more than killing the deer. Some hunters save their vacation time for the season and those who own their own businesses will sometimes shut it down. Cutting the shirt tail of someone who has missed a deer is an old tradition of dog hunting that has almost been forgotten. The tradition of smearing blood on the face of a hunter who just took his first deer has also almost been forgotten.
– Terry Jones, Dog Driving, [2]