Muscles in Movement 

Horses use their muscles to produce movement. Good movement and the co-ordination needed for jumping, galloping and dressage require the following … 

Muscle activation:  The motor nerve stimulates an action potential (impulse) to pass down a neuron to the neuromuscular junction. This stimulates the sarcoplasmic reticulum to release calcium into the muscle cell.
Muscle contraction
Calcium floods into the muscle cell binding with troponin allowing actin and myosin to bind.  The actin and myosin cross bridges bind and contract using ATP as energy (ATP is an energy compound that all cells use to fuel their activity).
RechargingATP is re-synthesised (re-manufactured) allowing actin and myosin to maintain their strong binding state.
RelaxationRelaxation occurs when stimulation of the nerve stops.  Calcium is then pumped back into the sarcoplasmic reticulum breaking the link between actin and myosin. Actin and myosin return to their unbound state causing the muscle to relax. 

Alternatively relaxation (failure) will also occur when ATP is no longer available

In order for a skeletal muscle contraction to occur;

 There must be a neural stimulus
 There must be calcium in the muscle cells
 ATP must be available for energy

Fitness training and schooling sessions should gradually become longer and harder, sometimes if a session is too long then muscle contraction becomes more difficult for the following reasons….. 

Energy system fatigue:  There is no more ATP left in the muscle cell so it can’t keep contracting.

Nervous system fatigue:  The nervous system is not able to create impulses sufficiently or quickly enough to maintain the stimulus and cause calcium to release.

Voluntary nervous system control:  The nerve that tells the muscle to contract stops sending that signal because the brain tells it to, so no more calcium ions will enter the muscle cell and the contraction stops.
Sensory nervous system information:  For example, a sensory neuron (nerves that detect stimuli how high a jump is) provides feedback to the horses brain indicating that a muscle is unable to provide the energy required.

Fitness training and schooling sessions are designed to make the muscles bigger and stronger, most of muscle tiredness is due to the normal depletion of energy, ie the rate of work cannot be maintained because the energy supply (ATP) has simply run out.