(This doesn't have anything to do with whether he had one arm.)
I asked a friend who does a lot of on-the-water stuff around New England what she thought about this guy and his suit. She said that ocean kayakers often wear exposure-type wetsuits in cold water or cold weather. They put them on before they start. Since you're mostly just sitting in the boat (even though your arms are busy) and possibly getting wet, you can get awfully cold. Sometimes people will pull them over their legs and up their body, but not cover their shoulders and arms.
She says she and her husband will wear a similar suit when they work on their sailboat because it's pretty easy to fall in leaning overboard to paint, and the water is damn cold in New England in the spring. (that's a quote

) They do carry the suits with them when they're sailing, though she's not sure they would have time to get them on in a real emergency.