What is the room temperature of water?

This is because the water conducts heat away from the body faster than air so you feel much colder.

For the same reason metal objects always feel colder than wooden objects when they are both at the same temperature as the heat conducts away from your hand faster and your hand feels colder.

Heat and temperature are not the same things. Water is denser than air, so at any given temp., there's more heat energy in the water. Or, if lower than body temperature, the water will DRAiN your own heat. So on a day of 100 F. air temps, you will feel even MORE uncomfortably warm, in a tub of 100 F. water.

Water removes heat from the body (and therefore cools it down) mainly by conduction and water has a high heat capacity and so doesn't warm up much when in contact with your body.

Air removes heat mainly by convection (if it's free to move) and this is a relatively inefficient process. If the air is trapped (like in the cells of a string vest) it is warmed very quickly by the body as it has such a low heat capacity. This feels warm your body.

Its a bit like walking on a tiled floor (conducts heat away from your feet quickly and so feels cold) and on a carpet (quite a good insulator, warms up quickly to your body temperature and feels warmer underfoot)

Because the heat transfer between water and your body is round about 25% faster than air and your body.

what is the temperature of the room?

you're body has to adjust, it's wet