Swimming with your horse can be an amazing summer activity. It's great to have a bit of guidance - especially when trying this for the first time. Here are a few tips from horse trainer extraodinaire Lauren Woodbridge, of Black Pearl Horses.
Be prepared to get wet. Don't get in the water with your horse expecting to stay on and only get your toes wet.
For first time horses leading them in from the ground or from a brave horse will help their confidence a lot. Sometimes they don't like the transition from dry to wet so bringing a bucket along and doing a bit of a pre-swim bath can help break the barrier. If you are on the ground watch your spacing as the horses can become quite exuberant with their front legs in the water.
When you get deep enough to swim, hold the horse's mane and elongate your body so you are swimming as well. Many horses get stressed when swimming. Staying seated on their back can make them sink and panic.
When they do start swimming they will nearly always turn back to shore straight away. So if you are on the ground make sure you are positioned in the centre of their ark and are prepared for them to turn and move quickly. If you are on their back hold onto the mane, give them room move and prepare for the surge forward.
If you are mounted when you enter the water and the horse goes down to roll, rather then punish them for having fun as well, put your feet down on the ground and simply stand up.