Making a horse slow down the trot is not as difficult as you might assume making them slow down the trot might be. To make a horse slow down the trot is often as simple as a few clear aids (cues) instructing them to shorten their stride or slow the pace of their stride.
For a horse that wants to burst into a out of control extended trot each time you ask for it from the walk, try this: From the walk, don't kick, spur, or whip,but simply put your shoulders back, take a deep intake of breath, and squeeze slightly. This is the trot cue for a well trained horse, using a stronger cue may scare them into a trot. If your horse still explodes into a too fast trot you may want to take them all the way back to walk to teach them to slow down their too fast trot. Repeatedly ask for trot, if they bust into it, take them back to walk, but if they take even a few strides of a nice, slow trot, praise them and let them trot on.
To slow down a horse's trot once in gait can be done several different ways. Some horses used to inexperienced riders may only respond to being "checked" by a rein, pthers may slow down their trot as a response to a rider sighing deeply and settling deeper into the saddle. For a more advanced rider, a horses trot can easily be slowed by simply "riding a slower trot" and altering the movements of ones pelvis from following the horse's movement to leading the horses movement into a slower trot. Less expereinced riders may want to try this method to slow down the trot at a posting trot.