The heat capacity of humid air is approximately given by:
$$ C_p = 1.005 + 1.82H $$
where 1.005 kJ/kg°C is the heat capacity of dry air, 1.82 kJ/kg°C the heat capacity of water vapor, and H is the absolute humidity in kg water vapor per kg dry air in the mixture. So the specific heat capacity of humid air is greater than dry air and humid air will take more energy to heat by a given amount.
But the difference is quite small. I think 100% RH at 25C is only about 2% water, and if you need to heat the room the temperature, and therefore the water content, is presumably even lower. Taking the 2% water content only increases the specific heat by about 3.6%.
Wind chill is really due to two things:
1) colder air moves across the surface of your skin, replacing the air you heated with your body: this in essence takes away the blanket of warm air you keep making for yourself.
2) As your body loses moisture through evaporation, there is a humidity gradient of stagnant vapor around your body. The higher the humidity of the air around you, the less heat you lose by evaporation.
The conclusion from these two things is that in situation 1 you describe, the extent to which the man feels hot depends a great deal on temperature. There is something called the "wet bulb temperature": if you have two thermometers - one dry, and one wrapped in moist cotton - they will read a difference in temperature, and this difference is a function of relative humidity precisely because of the above. This is frequently used as a way to determine relative humidity, and charts are published like this one:
This contains all the information you need to determine how hot your person in the desert feels, depending on the relative humidity. At 40 percent relative humidity, a temperature of 100 F will "feel like" 70 F. This will be affected by wind - if the wind flows faster, there will be less humidity gradient and you will get closer to the value given. Note that the "psychrometer" works when the thermometer is in motion (you swing it around at the end of a string!) because otherwise it would not "feel the wind chill".
But it follows from the above that if you have 100% humidity, there is no "wind chill" to be felt. In fact, you feel this in a sauna - while the air is dry, you can tolerate quite high temperatures (80C). The moment somebody drops water on the stones of the furnace, it can become uncomfortable for two reasons: first, the steam condenses on your skin (which is colder than the air) which releases a lot of heat; second, there is no longer any opportunity to lose heat by sweating.
Best Answer
The cooling effect of air will depend in the flow rate and thermal conductivity of air. The latter is in turn a function of temperature, pressure and water content. Counter-intuitively, if we keep pressure constant, the most water the less thermal conductivity, and the decrease in thermal conductivity is more significant for higher temperatures, as shown by the following graph:
A more detailed explanation of the causes of this behavior can be found at the original source of the image: electronics-cooling.com