I have or rather "had" a horse that did that. Give you my story and you see from there if you can work my solution into your training. I rode this horse, Scotty, when he was a breeding stallion, mostly arena riding & shows for his then owner. I bought this horse after his breeding career was over & he was a gelding. I took him out on a trail ride after he was all sweaty working in the arena. Was a blistering hot day, so I grabbed a beer for the ride. I wasn't paying attention as we ambled down the trail, but I did see a big dip with some water in it, figured he was going to just walk through it, I was chugging the beer, he jumped the big puddle, I had beer up my nose. I found out he didn't want no part of getting his white socks all wet.
Next spring I had one corner of my arena under water when the snow melted, perfect water training spot. I got him walking through the water with weight, seat, legs and rein cues, persistant & correct cues.
Last summer, I took my horse (his son) swimming, my husband rides Scotty (technically his horse) and tries to get him to swim, no dice. He did get him into to his knees but no further. I offered to try to get him to swim but hubby refused & said next year, he will have the skills to make him swim, we'll see. I am pretty sure I could have, but he wants to do it himself.