Water has a much higher Specific Heat Capacity than air, making it a far better coolant than air. Water absorbs heat like the coolant in your car engine meaning it can take the thermal heat energy our bodies give off, while still staying at a very similar temperature. Because the water buffers the air temperature, the range of air temperature near water bodies is often smaller than the air temperature range further from large bodies of water.
Sadly, you are misinformed - water has a specific heat capacity that is comparable to that of air: differing only by a factor of less than four.
What really matters is the difference in density. There we have almost a thousand-fold difference. So a warm hand in air loses much less heat than it would when immersed into water at the same temperature.
The ocean usually lags behind air temperatures during the seasons because of the relative heat capacities and masses of the ocean and the atmosphere. But It is true that at equilibrium, a hand in air will have cooled less than if it were in water. You may not reach equilibrium. It depends on how long you leave your hand there, on whether the hand is wet or dry, whether there's a wind, wind speed, the temperature differentials between your hand and the air and between your hand and the water, and several other factors. One big factor is the thermal conductivity of the fluid you're exposed to:
Air thermal conductivity 0.01486 Btu/(h ft F)
H2O thermal conductivity 0.352 Btu/(h ft F) -- about 24 times higher than air.
The water feels colder than the air because water is more conductive to heat. Short explanation: the temperature of your skin depends on the equilibrium formed by heat transfer from your warm insides to the skin, and from the skin to the outside. It takes 4 times the energy to heat up water than to heat air. Water also "feels" colder because water is a more efficient medium than air to cool our body down. Water has a higher heat capacity than air, which means that it takes more energy to heat water by 1 degree Celsius than it does to heat air by 1 degree Celsius Because the water buffers the air temperature, the range of air temperature near water bodies is often smaller than the air temperature range further from large bodies of water. Air will flow from high to low pressure and that will create a wind. The cooler air over the ocean will flow to the warmer air off the coast, creating what we call a Sea Breeze, thus making it feel a bit cooler when along a waterfront. The heat capacity of the ocean is much greater than that of the atmosphere or the land. As the ocean slowly warms in the summer, keeping air cool, and it slowly cools in winter, keeping the air warm. The reason the water feels colder than air is because water is the better conductor of the two. When you hop into that 60-degree pool, heat escapes your body much more easily than it would if you were standing beside the pool in 60-degree air. The major significance of Antarctic bottom water is that it is the coldest bottom water, giving it a significant influence on the movement of the world's oceans. Antarctic bottom water also has high oxygen content relative to the rest of the oceans' deep waters. The high heat capacity of water also explains why the temperatures of land near a body of water are more moderate. The high heat capacity of water keeps its temperature within a relatively narrow range, causing nearby coastal areas to also have a narrow daily and seasonal temperature range. Water warms up more slowly than air but can hold more heat – water needs 4 times as much energy to raise its temperature by 1ºC as the same mass of air does – so the ocean plays an important part in taking up energy from the Sun and stopping the Earth getting too hot.