A couple of friends have been inintentionally swimming with their horses
One, we were crossing a pretty shallow creek and he splashed a couple times, had a drink then before she could ask him to walk, he layed down.
The other time was when we went to the beach. My friend was riding her Standardbred and he likes to go and just stand in their dam and then roll in the sand, so when he saw sand and water in the same place, he got over joyed and went straight down and started rolling. Right infront of a lovely beach front restaurant - packed out for lunch time
I've walked my gelding through water a couple times and he's allowed to have a splash, but that's it. One day he thought he'd outsmart me and just go down, but he got half way down and was yelled at so he gave up.
NorthernMama is right though. They won't actually swim
unless the water is too deep for them to walk.