You are right, up north may be different. However I did this in Missouri in ponds on farms when I was healthy.
Down here they have riding clubs for the disabled. One in particular caters to those with spinal issues. We have a causeway that goes over to the Island, where the horses can be. During high season, there may be as many as 30 horses swimming in the gulf's causeway.
My first time back on, I slid off like greased lightening. I had forgotten how hard you have to press your knees bareback with a swimming horse. Came up sputtering and laughing, not the least bit in pain or worried. I have a piggy bank that I save money for, just for this purpose. Our season only lasts really for the summer too. Gulf temps are down now.
I plan to go again next summer. I am 62, and love this animal, and have all my life. ginnie