I've taken both horses (Ruby and Sugar) in the water and swimming. They both loved it but I can tell Sugar loved it the most. Not only did she love it but she definitely had trust in me and didn't lose attention to obey me while being in a different and new environment.
Probably the biggest reason a horse would try to avoid water would be fear. Fear of it being very deep or just fear of drowning wether or not 3 feet deep or a 100. Because they have monocular vision it makes it very hard to tell deep or far something is. Other spooky reasons like something might be in it that could eat them WHOLE!!!!! Not all of the time but most of the time when introducing a horse to water they'll be a bit reluctant to get in. BUT, they are natural swimmers! And are known to love swimming! Like me ;)
There's an old saying; "you can lead a horse to water, but you can't make him drink". Which is true. But I can teach them to want to be in the water. I can actually change their minds from avoiding water to dying to go in.
Now if the horse is afraid of the water, which a lot of the time will be the case, I'll prove to him that there's nothing to fear. I've said this a lot in the past but it's basically all it is, make the hard thing look easy the easy thing hard. In this case the dry land is the easy part and the water the hard. So I'll move the horses feet/work her on land and let him rest in the water. In the beginning I'll let him investigate a little the water by himself. If he doesn't go in then I'll keep adding pressure till he does. Then release as soon as he's in. Horses learn from the release of pressure, not pressure itself.
I'll lunge him around to where almost half of the circle will be in the water. But as much as I can and especially in the beginning I'll make it very easy for him to be in the water. Sometimes it takes forever to get a horse comfortably in the water and other times it hardily takes anything to get him in. It all depends on the horse. Every horse is different. When lunging and he's going around on land, if he slows or tries get out of it then I'll add pressure. Because that's where he feels safe but I want him to feel safe in the water too not just on land. So if he stays on land then it just means a lot of sweat and work. Another important part to this is to establish a starting point. A lot of mistakes people make (and I've made) is asking too much in the beginning. Don't expect he'll go right in. Don't ask for him to go to swim where he can't touch right off. If it's a very difficult horse, start smaller. Even if that means two feet have finally stepped in the water-STOP! Take the pressure away and reward him.