Explain why your hands feel cool if they get wet?

How hot or cold you feel depends on the rate at which your body is losing heat to the environment

Water on your skin acts pretty much like sweat. Water is more thermally conductive than air; therefore, the skin loses its heat to it much faster than it would to air.

Also, because water evaporates, it carries heat away from the skin and this increases the rate at which the skin loses its heat. The faster heat loss from the skin to water is what makes us feel cold when we are wet. But of course, the temperature of water has to be lower than the skin for this to occur, which is usually the case.