no burns, even sunburns, should be readily doused with cold water or cold anything! that increases the difference in temperatures and increases the burn. this has been tested and needs to be told. if you want to wet it, put burn in slightly warmed water and let the burn cool with the water, once both are tepid, you can add ice.
a folk remedy that helps slight kitchen burns is to stick it quickly in sugar as the crystals help disburse the heat.