You’ll find stretches of some form on most of the exercise plans I write, like most physios. But why do think there’s so important? Well firstly, stretches are easily performed well by any one regardless of your training ability. Animals will follow something tasty! Secondly, they aren't time consuming so achievable by any owner, you don't need to tack up or brush them, it's 5 minutes of your time in a day.
Active stretches are when the horse does the work to form the shape, think yoga poses! The horse recurruits muscle effort to move joints to the maximum range of motion. One set of muscles contracts and shortens and the other relaxes and are stretched. These can be used to relax muscles but also to train and strengthen the other set of muscles. These are often beneficial for posture of the back where the abdominals are worked and the spine is stretched and lifted. Active stretches encourage blood flow to an area so can help promote healing as well as stimulating nerve pathways that can aid posture changes and proprioception.
Passive stretches are when we move the joint through the range of motion. This is normally with leg stretches as other joints are too heavy for us to manipulate (we're stretching not performing chiropractic's). This aids flexibility and recovery of muscles in helping maintain normal length. When muscles are worked hard, there are micro tears in the muscle fibres. This is what causes the next day ache! When these micro tears repair, the muscle fibres can be shortened so stretches like this can help maintain the length and functionality. This is why passive stretches should always be performed post exercise and not before.