IMHO, trick training is okay if done right. The problems that I see are when horses know tricks better than simple manners. A friend of mine has a horse who knows how to bow and to lay down. That horse will also lay down during a ride when she decides that she wants rewarded for something easy. That mare can be pushed out of it when she starts acting like she wants to lay down, but it adds a layer of difficulty to things. Tricks like rearing on cue and pawing to count can turn into outright vices or dangers if not handled with care.
I haven't taught any "dramatic" tricks to mine. My old Johnny could shake his head "no" on cue, and my sister's horse can "smile" on cue. They're simple tricks, kind of cute (the horses score big points when the city-dwelling relatives visit), but almost can't be turned against me farther down the line.
I'll let someone else tackle the practical issue of laying a horse down as for a trick. The "best" way I've seen is to pick up a foreleg and sort of guide it back, encouraging the horse to drop down, and rewarding the horse for relaxing down and back until he relaxes down to the ground. Looks pretty low-key and non-forceful.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown