When I was a kid we used to swim ours in the lake by our house... we knew the bottom, because we swam there ourselves...
Chico, my mustang, would swim clear out over his head, and really, I'd grab mane and mostly swim along side, until he headed back to shore and I'd swing my leg back over before he touched bottom. I had been known to swim him, take him out and shampoo him, then swim him to rinse. They get really super clean that way! Immersion! He enjoyed it, I haven't had a chance like that, or access to a lake with a horse, since.
It's not for the faint of heart, we swam bareback and without tack (halter and lead rope) in bathing suits! But as hot as it is there, I might have considered swimming fully clothed!
At the ranch Jenny and I use to work at we were told all the ponds were safe to take the horses in. so we swam them there. Well Jenny did. I'd go out quit a ways, but never were the horse could touch. Those horses were use to it so it didn't bother them. Harley doesn't even like stepping in puddles....I don't know what he would do.
Becky