The best way to keep warm in cold waters is to warm up before entering the ocean.
Paddling like crazy on your board won’t help at all in my experience. You just get exhausted but not warmer. You have to get warm before getting in the water.
I personally use this kind of warm-up routine to store heat up in my body:
I know I’m ready the moment I’m sweating in my wet suit and feeling really warm.
I found that squats help me generate a lot of heat. That’s because they solicit the biggest muscles in the body: the quadriceps. I guess that’s why body boarders don’t really feel the cold, because they constantly use their quadriceps.
Another discovery: no need to wear a 5/3 mm wet suit. I tried: it keeps me warm but the neoprene is so thick paddling becomes exhausting after 30 minutes.
Icing on the cake: warming up helps you surf at your best from the first wave and reduces the risk of injuries.