Water is roughly 20x more thermally conductive than air, so it takes heat away much faster. Air also takes heat away from your body, but your body can make the heat back faster than the air can take it away.

It’s because of heat conduction. Air is a better insulator than water, so it transmits less heat out of your body. Water is a poor insulator and transmits more. You feel cold based on how much heat leaves your body.

Water is a much better conductor of heat than air. So whatever the difference in temperature, your body will more quickly move towards the temperature of the water than it does with the air.

That is also why boiling food tends to cook it quicker than making it even though boiling is done in lower temperatures.

it's like this..

it's the same reason why holding your hand above a red hot pan is less hot than putting your hand directly on the red hot pan.

the transfer for heat, or cold (actually thermal conductivity of heat, or energy, is transferred to a colder area, or an area with less energy) is more efficient with liquids & solids, than air.

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To add on to your answer, we don't feel temperature, we just feel the heat transfer rate. That's one of the reasons we have a "feels like" temperature in our weather forecasts.

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