When you feel hot, you perspire so as to benefit by evaporative cooling. As the relative humidity gets closer to 100%, the sweat cannot evaporate and evaporative cooling becomes less effective.
Liquid water is a much better conductor of heat than air (even humid air) is, so if the water is even a few degrees cooler than your body, you feel cold because the water is efficiently conducting your body heat away. A room at 60°F (15°C) feels slightly chilly; in 60° water, you will die in a few hours.
The same is true of metal. On a very hot or very cold day, touch a metal pole and compare it to the feeling of a wood post: it will feel much, much hotter or colder respectively, because metal is a much better conductor of heat than wood.