I use a modified version of a technique that Teddy Lancaster told me
about some years ago.
You need two coolers -- Teddy recommended wool but I use polarfleece so
that I can just throw them into the washing machine.
Put one on top of the other, and then put on two elastic
surcingles so that the fabric is snug all around, including the horse's
belly.
Give the horse some hay to munch on for perhaps ten or fifteen minutes, and
**voila** the inner cooler is dry -- as is the horse -- and the outer
cooler is quite wet. Brush the horse a bit to get rid of the dried
salt.