The core muscles is a term banded about quite a lot but what makes up the core muscles of a horse? Well quite a few in fact. The core muscles are the muscles that stabilise the back and pelvis. They include the abdominal muscle group, sub lumbar muscle group and the epaxial muscle group.
A strong core is important for horses as it is in humans. By developing a strong core a stable foundation can be developed to allow the horse to be balanced while moving. This reduces the chances of injuries as your horse will be able to cope physically with changes around them such as uneven surfaces or slipping. It also helps with posture and allows your horse to manage the weight of a rider by being able to lift through their back.
Below is a brief summary of the muscles that make up your horses core in part two core exercises will be described so that you can help strengthen your horses core.
Abdominal muscles

Rectus Abdominis
Origin: Sternum, xiphoid process, costal cartilage 4-9
Insertion: Prepubic tendon
Function: Aids in defacation, giving birth, and expiration. Supports the abdomen and flexes the back
Transversus Abdominis
Origin: Medial surface of asternal ribs thoracolumbar fascia, transverse processes of lumbar vertebrae
Insertion: Aponeurosis to linea alba, xiphoid cartilage
Function: Aids in defacation, giving birth and expiration. Supports the abdomen

Internal Obliques
Origin: Tuber coax and inguinal ligament
Insertion: Aponeurosis to linea alba, ribs 18, costal cartilage 14-18 and prepubic tendon
Function: Aids in defacation, giving birth and expiration. Supports the abdomen

External Obliques
Origin: Costal part lateral surface of ribs 4-18. Lumbar part thoracolumbar fascia
Insertion: Costal part linea alba and pubic tendon. Lumbar part inguinal ligament and tuber coxae
Function: Aids in defacation, giving birth and expiration. Supports the abdomen
The abdominal muscle group as you can see mainly supports the abdomen and are involved in bodily functions as in breathing and going to the toilet. The abdominals also help support the trunk when exercising. When engaged they help lift through the back giving the horse a top line that can deal with carrying a rider and complex movement patterns like jumping or dressage moves.
Sub lumbar muscles

Iliacus
Origin: Sacropelvic surface of ilium, pelvic surface of sacrum and tendon of psoas minor
Insertion: Lesser trochanter of the femur
Function: Flexes and rotates hip joint laterally, moves limb forward

Psoas Major
Origin: Ribs 17-18, ventral surface of bodies and transverse processes of lumbar vertebrae
Insertion: Lesser trochanter of femur
Function: Flexes hip joint, moves limb forward and laterally rotates limb
Fuses with iliacus to form iliopsoas complex

Psoas Minor
Origin: Bodies of Thoracic vertebrae 17-18 and lumbar vertebrae 1-5
Insertion: Ilium and tubercle of psoas minor
Function: With the vertebral column fixed it draws the pelvis forward. With the pelvis fixed it flexed the vertebral column
The sub lumbar muscle group connects the back and pelvis. It helps stabilise these two components allowing them to function at a higher capacity without sustaining an injury. There are other muscles like the gluteals that also help but these will be discussed another time. The sub lumbar muscle group are the deeper muscles that function as part of the core.
Epaxial muscles

Multifidus (thoracic and lumbar part)
Origin: Artucilar and maxillary processes of sacrum, lumbar and thoracic vertebra
Insertion: Spinous processes of thoracic and lumbar vertebrae, spinous process of cervical vertebrae 7
Function: Bilaterally extends back, unilaterally bends vertebral column laterally and rotetes

Longissimus (cervics and dorsi)
Origin: Cervics portion transverse processes of thoracic vertebrae 1-7 and thoracic part of longissumus dorsi. Longissumus dorsi wing of iliac bone, spinous processes of sacrum, lumbar and thoracic vertebrae
Insertion: Cervicis portion transverse processes of cervical vertebra 4-7. Longissimus dorsi transverse and maxillary processes of cervical vertebrae 4-7 and tubercles of ribs
Function: Extends back and neck, stabilises vertebral column
Iliocostalis
Origin: Transverse processes of lumbar vertebrae 1-5, cranial margins of ribs
Insertion: Cuadal margins of ribs 1-15, transverse process of cervical vertebrae 7
Function: Bilaterally extends and stabilises vertebral column. Unilaterally bends back
The epaxial muscle group are located along the back unlike the abdominal muscle group. They solely focus on stabilising and moving the back.
So this is a brief summary of the muscles that make up the deep core of the horse. Hopefully it will allow you to have a better understanding of their role and location to help you work with your horse. To further this understanding the second part will discuss exercises that will strengthen all the above muscles.