I'll hose mine off every single summer day if they are hot and sweaty.
If I am working a horse, that's mandatory. Never put up a sweaty horse, that's just nasty
I also like to use Absorbine Refreshermint sponge bath which cuts the sweat and leaves them feeling great and smelling super nice
Full shampoo baths once a week usually for everyone
For that special itchy horse of yours I would try to find the problem; it may be lice or skin fungus, rainrot, lots of things but for that you can use Betadine shampoo or a medicated shampoo