Cold water on the major arteries!
Same! I make sure to walk my horses out until their breathing is calm and normal. Then I'll untack and curry quickly, then hose. I usually start with the legs and then focus on chest, neck, and saddle area. Going back and forth to all of those areas. I also usually encourage my horses to put the hose in their mouth to help rinse all the residue from having a bit in. :)
I always walk my horses until breathing is normal, then hose him for a solid 10 - 20 minutes focusing on the legs, neck/crest, and dock. I will especially scrub gently with a curry comb in the girth area while hosing.
Duration of hosing depends on how long and intense the ride was.
My thought process is that, if you wait until the horse's breathing goes back to normal, the sweating will cease and that way you don't have to worry about sweating continuing after you hose.