My son is almost 2 and he gets colder faster in the "cover-all" SPF 50 2-piece suit I would rather he wore to help shade his skin from the sun. He does a lot better in a swim diaper and sunscreen, so that's what we do now. I've never seen an actual "wet suit" for kids, one that traps water between the skin and the fabric so the body can heat it up, is that what you have?
ETA: After reading the other posts, my son is also little. 26 pounds at 22 months. I looked at the link you PMed me of the suit, I say try going without it and see what happens, because the only way that would help keep him warm was if it trapped water. Quick-drying fabric is still cold until it's dry, IMO. Good luck!