I have never had a horse go down with me personally, but we used to ride with a friend who had this Appy who would drop as soon as he was four feet (not depth either) into any size water puddle! His owner always had to keep him moving, and even then, he sometimes got the best of her!!! He would go into a trail ride a brilliant chestnut leopard, and come out a brown/black splashy type! Hahahaha
Other than him, I don't think I have ever had one or known one that would go down just because he wanted to play in the water. I have had several, though that LOVED to swim...so I would take them down to a local sand pit that had those awesome clear pools, and strip the saddle off, and in we would go...it was magical!!!
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."