Yes you should take your clothes off. They impede your movements and provide you with no insulation.
They don't provide insulation, and only serve to make you wet and extract heat from you. Just like a wet towel wrapped around a champaign bottle.
Once someone is out the water wet clothing should be removed.
New cold water will seep through much faster than your body can warm it. Even if you gained a fraction of a degree from tightly fitting clothes you'd lose much more than that through lack of mobility.
See: http://en.wikipedia.org/wiki/Wetsuit
". . .a thin layer of trapped water could be tolerated between the suit fabric and the skin, so long as insulation was present in the fabric in the form of trapped bubbles. In this case, the water would quickly reach skin temperature and the air in the fabric would continue to act as the thermal insulation to keep it that way. The suit did not need to be dry to be insulative."
The idea behind their operation is that you have a thin film of warm water around your body, isolated by a waterproof neophrene layer. So there's: The Sea -> neophrene -> Warm water that doesn't freely mix with the sea -> You.
That doesn't work (as deadmansshoes thought) if you're wearing normal clothes instead of a neophrene layer. In that case the water next to your body is constantly being replaced by new & cold water, faster than you can heat it up to provide you with insulation.
Both wetsuit and drysuits depend on there being a layer next to your body that you heat up. With wetsuits this is a layer of water that doesn't get swapped out, with drysuits it's a layer of air + rubber.
The article suggests you won't be able to swim so struggling to take your clothes off seems like very bad advice.
Several layers of clothes, and even a semi-waterproof jacket or anorak will trap water - and air which would help with bouyancy.
A fraction of a degree could be all important - there is a tipping point where a fraction means living or dying.