It depends on your horse way of life : stable, field, rug or not, …
When you shampoo a horse, you remove the grease that covers his coat and protects him from external aggressions.
If your horse lives in a stable, with a rug on and you groom him softly, there is no harm in washing him regularly (several times a week for example).
On the contrary, a horse living in a field, without a rug, will need to protect himself naturally from bad weather (rain, snow, sun). In this case, you’ll need to be careful not to wash him too often, only if necessary.
Moreover, horse skin is thinner than the human one and has a less acid pH. To reduce bad reactions and respect skin sensitivity, it is essential to use horse adapted products.
I hope this helps !