canine vs. equine

Our new dog Rocky is proving to be a quandry. He is a very sweet dog, loves people and wants to please. He is great in the house and on a leash. When the leash is off, so is he. Off to the neighbors, off chasing deer in the woods, etc.
I know horses and horse training. I can teach a horse to come when called, but dogs are a different scenario. Some say it is the difference between a prey animal (horse) and a predator (dog).
Yesterday, Rocky decided to run off through the horse pasture, across the road and take a tour of the neighbor's yard. I saw him do it, I called, he ignored. I got a leash and started walking towards the neighbors. When he saw me coming and I asked for him to come, he looked right at me and said, "sorry I've got other things to do," and kept going. I eventually caught up with him and brought him home.
I once knew a man with a wandering dog. His idea of training was to beat the dog when it came home. All the dog learned was not to come home. I do not condone beating any animal for any reason. Discipline is one thing, beating is a whole different issue.
Discipline implies calm, consistent behavior specific to the issue. Beating implies a human who has allowed his anger to control his behavior.
I know that anger has no place in horse training and I'm sure it has no place in dog training. I don't want my animals to be afraid of me, only to respect me.
There are some times when I try some of my horse training techniques on the dog. In horse training, when the horse is doing something you don't want him to do, you ask him to do something you want him to do instead. This works with Rocky if we are in the house or on the leash. It works well. So far, at liberty it doesn't work.
I know that liberty training with horses is started in an enclosed space, then transferred to total freedom. So far, Rocky is good in enclosed spaces, but hasn't let it transfer to total freedom.
Yes, he's only two years old and we've only had him for a few weeks. Time is important. He still has puppy brain, with grown dog speed.
At least he knows where home is. When he took off after the deer, he made a big loop through the woods and field and came back to me after about 1/2 hour.
It's a small step in the right direction.
What's your dog training challenge?
What's your horse training challenge?
Got any tips for Rocky?