If your dog is comfortable around horses, you're off to a good start. Dogs who are overly cautious of horses dont usually tend to want to follow.
If your dog is cautious and wary around horses, work first around the barn by leading yor horse around and encouraging your dog to follow right along. Treats come in handy.
Really reiterate the "come" command. I always use treats. Teach your dog (off leash) to stop whatever he's doing by calling his name. Soon as he looks at you, throw him a treat. That was he associates his name with a treat. (if your dog is food oriented, I have labs so its easy, heh heh!) It's so annoying when you call a dog and he completely ignores you, especially when you're powerless on a horse.
I have a 6 month old lab/pit puppy who I started riding out in our jump feild and had her start to follow me around.
I would take her & her brother(as soon as about 3 months) and my older dog out for walks where we trail ride, off the leash, and whenever she got too far ahead, I'd call her back, throw her a treat and praise her for coming back. That way your dog already knows the drill when you hit the saddle. If your dog tends to just ignore you and run around and pay no regards to you, ignore your temptation to put him on a leash. Watch him like a hawk and if you feel he's about to take off, call him back.The more you catch him having the urge to run the more he'll learn he's not allowing to. Be patient and call him until he comes, and reward with a treat. Leashes dont teach them to stay with you, I dont think, only forces them to so they never learn to behave off the leash.
It also helps to take other dogs that know how to trail ride with you so your dog can follow and learn that its a fun thing dogs do.
Also, your first few rides dont go too long. If you go too long and your dog tires out, it spoils the fun for him. So go a few times on short rides until you feel like hes enjoying himself and gradually build the distance. You want to make it a fun, positive experience so your dog wants to come.
One more thing, I had a dog that was super hyper and really enjoyed running way too far ahead of us. One time we took her up to a friend's in the mountains and she high-tailed it too far away and wouldnt come back. I about had a panic attack, thinking we lost her for good. A little before we got back to the trailer, there she was. Looking quite unhappy w/ herself. After that she always stayed close in fear of getting herself lost.. Sometimes they need a scare like that to teach themselves to stay close with you.
I hope that helps! I've had a bunch of experience w/ this, so if you have q's feel free to ask!