For the horses, slow and quick time correspond to a walk-march and a sitting-trot, respectively.
From the en.wikipedia.org
You also have to have great core strength, especially when sitting the trot.
From the economist.com
Except in saddle seat riding, rider's shoulders maintain a slight forward incline throughout the rising trot, instead of the upright, vertical position seen in sitting trot.
From the en.wikipedia.org
Collected walk, trot, and canter were required, as was extended trot posting followed by collected trot sitting.