Michael sent this great question. He stated correctly that humidity makes you feel warmer in the summer and wanted to know if it made you feel warmer in the winter too.
The quick answer for outside is no, it doesn’t work the same as the summer. The reason why higher humidity makes you feel warmer in the summer is because it interferes with the bodies natural ability to cool. When we are warm, our bodies sweat. This moisture on the skin is exposed to evaporate, and it is this evaporation that steals some energy from our body and makes us feel cooler. Think about how much cooler you feel stepping out of the shower due to this evaporation. So when the dewpoint is higher, the sweat will not evaporate as much, hence you lose that cooling.
In the winter, dry air allows for any moisture to evaporate faster. Wind enhances this. So drier air will cool you even more. When it is damp, there is more water vapor, even at times drops of water in the air. Water conducts energy much faster than air. This is why you are so much cooler in water that is 65° than air at 65°. So a moist day would conduct the cold to us better.
Now keep in mind, my qualification for the answer was outside. When you bring this damp air in, the amount of moisture (the dewpoint) stays the same. So when we heat this air, the difference between the air temperature and the dewpoint is larger than outside. So what was damp is now dry and your sweat would evaporate quicker and you would feel colder. So running a humidifier in the house would help you some, even on those dry days.