My draft has some leading problems...

My big guy (17hh, 5yo gelding) has a terrible habit of running off or dragging people when he's being led. If he wants to go somewhere, he just goes, no matter what I do. It happens mostly when I'm leading him outside and he likes to get away from me and run down the trails. I'm worried that he could hurt someone or run out into the road.

What do I do when he does that? I figured reprimanding him after I catch him again would only make it worse, so I just carry on leading him wherever I was taking him.

Sounds like a serious lack of respect issue. You will probably have to re-start his ground manners as it seems like there are holes in his training. No matter how big he is, he needs to understand that YOU are the boss.
My friend's standardbred was like that and this is how I fixed it. I put the chain over her nose, and when I was leading her, if she pulled away, I would lead her into a tight circle and just keep circling until I had her attention. It is a very long and frustrating process, but sooner or later she got the idea that pulling/barging= circles.
If you don't like the idea of the chain, put his leadrope on, and when he tries to barge ahead, tug on the leadrope over and over and ask him to BACK UP. You just have to be really firm, as you are right, someday he really might hurt someone. Good luck!

So you need to teach Whoa - start at the walk (no rider) with a leadline standing at the horses left shoulder, step forward. Horse should immediately step forward with you, then say WHOA while stopping. If horse does not stop immediately snap the lead down (1 quick jerk) and repeat Whoa. Do this in a place where he normally would stop without a problem. (I strongly suggest starting with a chain OVER his nose. When you jerk down it’s loose chain then 1 QUICK jerk, back to loose chain – don’t hold – horse is stronger than you are so never use force.)

Once he does that (i.e. reacts immediately to YOU) then migrate from where he'll willingly stop to places where he is more easily distracted. Stop/walk MANY times with a few steps in between. Gradually add more walk steps but remember - he must ALWAYS halt when you halt.

Sequence is you halt, then (if needed) you say WHOA then (if needed) you snap down on lead. Idea is he halts WHEN you do and at (or slightly behind) your shoulder - NOT in front of your shoulder.

If he stops in front of your shoulder, step in front of him and make him back up (AT least TWO steps) immediately.

OK - when you've gotten his respect on the ground start it from his back. This time when you sit deeply in the saddle press straight down with both stirrups then say WHOA. Do NOT lean forward or back - rider MUST be straight up and down (think of standing in the stirrups and that will place your body and legs in the proper position). Use WHOA if he's slow to respond to halting from your riding.

This will take a while as you're teaching him - you didn't learn to read in 1 day and he won't learn to perform a perfect halt in 1 day either - it's repetition so you MUST be consistent EVERY time you ride and lead him.

Get a rope halter on him and when he goes to run off you need to get real aggressive with him. Jerk as hard as you can on the end of the rope and try to rip his head off. You will actually do very little to him but if you can get him to face up you can stop him. Practice getting him to disengage his hindquarters and step over with his front. Get him walking around you on the end of the lead rope and move his hind end away while his front end faces toward you then make his front end step over and go the other way. Do this several times untill he is good at it then take him out and practice it. If he tries to run off then do what I suggested in the first part of this post.

when i had a loan horse he used to do this with me the whole time, he would be running to get back to his field. i would do circles with him and walk the other way for a few strides then go back on course,. it helped me a lot

I had the same problem with a massive OTTB I used to ride. If he tried to run off I'd either yank the rope or grab his halter and just spin him around. My usual technique however was to back him up several steps, say woah and step away. If he moved an inch, I'd back him up some more. If he stood, even for a short moment, I'd say good boy and pat him. I did this consistantly and I was actually able to put a bucket of oats down infront of him without him charging at it. He'd wait for me to say go, or walk before moving up to eat.

Thanks, everyone.
He is a little better with a chain. I'll try the circling thing next time. :)