Generally speaking, the process of pronation and supination is falling forward in pronation and preventing the fall in supination. This is repeated in gait to have locomotion.
However locomotion on an incline shortens the falling forward gait, while a decline lengthens the falling forward gait. Both require great precision in placement of the limb and greater load on muscles in propelling the body up and preventing it from falling too far forward.
Going up means muscles involved in propelling upward must generate more force, while going down means muscles must prevent falling over a greater range of motion. The weakness of these tissues is often the prominent reason going down is more dangerous. There is general fatigue, but having these tissues doing all the extra work requires a specific perspective in training in keeping them strong on the ascent and descent.
The muscles groups generally involved in pronation, or placing the body in a forward fall, include trunk flexors, hip flexors, hip rotators, hip adductors, knee flexors, shoulder protractors, adductors, and depressors and elbow flexors. The muscle groups generally involved in supination, or propelling the body or preventing the forward fall, include trunk extensors, hips extensors, hip abductors, knee extensors, shoulder retractors, abductors, and elevators, and elbow extensors. As you may notice, trunk rotation and trunk side bend are not listed. This is due to their involvement in both motions during gait. Also, in the various different climbing steps, these can switch places.
Knowing these areas of the body and generally how they are involved in moving us forward offers us insight in how to train them. Some may bias toward precision motion training while others may need training in producing greater force output over time.
Breaking down the parts of the sum to train is the focus we take during the off season or for beginners trying to find how their body handles this new environment. When the parts are strong, then we move into compound motions involving the sum of the parts we put together from the previous training period.