I've only gone bareback, which is fine if you have a good grip on their mane and with your legs. I've gone in a lake and far enough out where they can't touch and I was just floating above their back. It's a blast once you get good at it. I also only go in a swimsuit and shorts, so your skin provides some grip against their wet hair.
Just make sure you have a good hold if you're going down any deeper than where they can touch. Many will try to lunge back up out of the water onto shore, which is where most of the people I do this with slip off.
Another thing to be wary of: just how much your horse enjoys swimming. My username was picked after a mare I love. She got her name because of how much she loves water (Poseidon is the god of the sea and horses..and it fits a mare that loves to swim). She will walk in until she's about knee deep and has attempted to roll in it. Not good for her rider.