Interesting one. Having spent the majority of my horse life handling racehorses, I can tell you that they always
walk beside me, never behind. I walk just in front of/at their shoulder and keep them on a relatively loose line, just dangling from their headstall to my hand but that slack can be taken up mighty quick if need be.
Simple reasoning being that regardless of which way they jump, strike, buck or rear (all possibilities with TB's when they are at the track) you have more control at their side, more warning that they are about to do something funky and you can see what they are plotting quicker.
Those suckers move QUICK when they want to be goofy, obviously you can't compare racehorses to all horses as it is a different kettle of fish.
As for training a horse to walk behind you, I am of no help - sorry! Why does the owner want the horse to lead in this manner? Just asking out of curiosity; to each his own