Update. We've made progress. A couple of things that helped...
First of all, I am using lukewarm water instead of cold, as PlainandTall recommended above. I think this made an enormous difference.
Secondly, I'm working with him in a halter and leadrope. Before I realized he had an issue with water, I put him in the cross ties. (Wrong. But I didn't know.)
Then I tried it with him totally at liberty in the round pen. I had a hose long enough to stay with him. That wasn't a terrible idea; but he ran from me some, and I really didn't want that. Mostly I stood next to him, one hand on his withers and one hand holding the hose (away from him), and that went OK.
But the best was when I put the halter and leadrope on him. He could still move around, but he couldn't run away from me.
I also let the water splash into a bucket in his stall for about three days straight; and he did get used to this. (This is a stall he can leave if he likes; but the food is in the stall.) But, as you can imagine, it made an enormous muddy mess! I couldn't keep that up forever.
But what really helped was not starting with his feet (as Chestnut Run suggested). I started with his MOUTH! He likes that! Now I've only gotten as far as his mouth, his muzzle, and his nostrils so far. But he likes it! He's so cute trying to chew on the water. He'll take the hose way up into his mouth (like a wormer, which he also likes).
I have high hopes that he's going to enjoy baths before long.
I've had luck with holding the horse in a pretty open area (not cross ties) and just holding the hose in my hand. The horse can circle around me all it wants. As soon as they stop circling, I turn off the hose. Once they are comfortable with that, I start hosing the feet. Again - horse can circle all it wants, I just follow it with the water. Horse stops, I stop hosing and lots of praise/treats/whatever. When the horse tolerates the feet, move up the legs and over the rest of the body.
Timing and coordination are key. Don't try to push too much in any one session and fry his brain -- let it take however many sessions over however many days.
This^ ....You should never remove the pressure(hose) till you get the desired response....which in this case is standing still......then you remove the pressure......once you have the horse standing quiet for a second ....then start requesting longer and longer......and then working to having him standing still while the water is on his body.......I usually work with a long hose in the middle of a big clear area......so horse can circle with out running into anything.