As everybody, I shower when it is hot (the whole body) and when it is colder, I just wash the legs and tail if necessary
To remove dirty marks, sweat and mud, I shower the legs, hearth girth and sometimes the neck. When it is really hot, I shower the entire body almost everyday, it depends of the temperature.
In the summer time almost everyday and before a show, so it can be once a week or less.
As Mark, when it is super hot and humid or after riding. In the winter time, if it is not too cold and if my horse did important efforts, I shower the limbs.
I shower when it is really hot or after an intense training. And I use shampoo when he has dirt marks or before an important show (especially for the tail).