I grew up on a farm in coyote country in South Dakota and often saw coyotes harassing dogs. For example, we had a nice picture window at the breakfast table and several times were treated to a scene of several coyotes chasing our relatively tough German Shepard mix dog up on our picnic table. The dog was scared to death of them. Normally, I saw that dogs were not a match for a group of coyotes and generally left them alone. The snow there gets hard on the top layer and coyotes/dogs can run on top of 10 feet of snow just fine. The only dogs I ever saw consistently chasing and harassing coyotes were grey hounds. My neighbor raised and trained them and he would let them run the coyotes in the snow. They loved it and did it all the time... never saw one kill a coyote but they loved to catch them and snap at their heels. Most dogs have a hard time keeping up with coyotes but grey hounds literally sucked them up. I also saw a pack of about 25 coyotes flying across the deep snow covered prairie about 300 yards out once. I pulled up and shot the lead coyote. When I went to pick it up, I was surprised to see that it was a big male German Shepard that someone had apparently dumped. It seemed to me that other than these instances, most farm dogs didn't care to chase coyotes.

well if they are the right dogs size wise. i have some step by step photos from a i guy i talk to on line ,with his buddies hounds running, baying,and dispatching a yote . beagles wont fare well for this job.

Most of the coyote hunters here in Maine use Walkers and they will stay on the track until you pull them off. Depending on the conditions, they could be practically in sight of the animal or further than a mile behind. On heavy crust with a light snow cover you would be shocked at how well a good dag can stay close.