How to get an A on my evil physics final
Take off your socks and shoes, and spray just a light mist from the spray bottle onto your feet.
Walk briskly, but don't run, across.
Why? Well, first, the reason you don't wear the boots. Human feet are slightly porous, where leather boots are generally covered with waterproofing. Waterproofing means that the water won't reliably stay on.
Secondly, the reason you don't wear socks. Socks are too porous; they would get soaked.
What you're trying to do is get the water on your feet to create a film boil. At the temperatures we're talking, water doesn't go straight to steam all at once (though ice would, because sublimation is a different process). It forms a film of steam bubbles which act as an insulator. Too much or too little water would ruin the effect, but a light spritz on the bottom of your feet is just about right.
Why walk briskly? Reduces the time you're in contact with the coals, and thus the conduction.
Why not run? Trip, and you're really in trouble.
What about radiation? The coals aren't that hot. If they were hydrogen plasma, yes, radiation would fry you with or without film boiling. But the coals will radiate very little.
Do the boots help? Not a bit. They're waterproof and leather burns.
Does the ice help? Not nearly enough heat capacity to cool the coals. Actually, if you started to throw the ice, I'd stop you and fail you on the spot. The sublimating ice would create a thick mist of very dangerous superheated steam. That's probably the only way you could die from this test.