Well let's see...
For one, he dunks his hand quite awhile before he does the test. If he really wanted his hand to be cold, he's dunk it, dry it, and do the test. Not wait all that time for his hand to warm up.
Second, what would it accomplish anyways? Stick your hand in the oven and tell me if it hurts. Now dunk your hand in ice water and stick it in the oven and tell me if it hurts. Now wait a minute before you stick it in the oven.
Third, the bulk of the lighting is focused at a very small area right at the tip of the blade, an area that his finger is in for an extremely small amount of time. The rest of the light is nowhere near the intensity of that spot.
Fourth, in the woodnet post, he states that after a few seconds, the heat from the light starts to burn his hand. Well if you look at the video in real-time, his hand is under the lights for about a second. By his own statement, that's before it starts to burn him anyways so why hedge your bets with the ice water???
And fifth, why are you concerned about some heat on your hand when YOU ARE ABOUT TO PUT YOUR FINGER INTO A SPINNING TABLE SAW BLADE.