I agree with Pikabike - you are in the worst of both worlds. Going hard you will be creating a lot of heat. But in the water, you will freeze fast. So you need a way to allow for both, which is hard. An unzipped wet suit that you could quickly zip back up when you are in the water seems like a good way, if you can make that work.
Most competitive surf skiers do not wear much, if anything. And there have been deaths of racers during practice sessions due to this. So I am glad to hear that you are considering options.
Staying close to shore has limited benefits. Water close to freezing only gives you a few minutes of swim time for an uninsulated person before your body stops sending blood to your arms and legs (instead keeping it in your core). A couple of failed tries at getting back on and you have used up your time, so swimming now isn't an option. Thermal protection extends the time. A 3 mm wet suit probably stretches that to maybe an hour. Keep this in mind, as the suggestion below of staying close to shore may not be as good as it sounds.
Sport Cases (Electronics)
Kindle / iPad Cases
Bent Shaft Canoe Paddles
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